This took a while. Sorry about that by the way.

As you can probably tell, I'm not a professional writer. In fact, I'm nota professional anything yet- I'm still a teenager. So, criticism is welcomed. As long as you keep wanting it, I'll keep writing it! Also, I'm British, so apologies for any readers over the pond who spell words differently, or say pants instead of trousers.

SPOCK'S POV
The Vulcans eyebrows raised as the frozen water crystals- snow, shifted and displaced beneath his feet. He tested the ground before he put his full weight down, the logical thing to do.
He was wary as to the snow, and rightly so. Vulcan, the world he was raised on, was a desert planet. Snow didn't fall on Vulcan, the high temperatures wouldn't allow the droplets of water to freeze. He recalled the hot dry sands and baking rocks of his homeland, and felt a pang of emotion.
Shocked at himself, he shut his eyes and attempted the briefest meditation session he had ever had, lasting all of ten seconds. The emotion, he remembered from his days as a conflicted child, was longing. It wasn't that he hadn't experienced any emotion since he was young, he was not a computer, as much as Sarek had tried to drill it into him. It was just this particular emotion was far from usual in him.
"Commander?"
A sudden, concerned question broke into his rivière, and two seconds later his eyes snapped wide open, and he winced as his dilated pupils contracted rapidly against the startling white light.
"Are you alright?
He looked in the direction the voice was coming from, and angled his head slightly downwards to meet his gaze to Cadet Uhura's, as was customary to Terrans.
"Indeed,"
He stated. Then he oddly felt as though he should give an explanation.
"I apologise. I was merely processing the new experience and information. "
He shocked himself at this half truth. Vulcans do not lie. But, technically, it wasn't entirely untrue. He was processing an experience and information,he told himself, but still he felt as though he has corrupted the Cadet.
"Gather everyone, come and stand around me."
Called the loud voice of the man in charge of the mission. Captain Holden was a rather tall, strongly built man, with defined musculature and a face, Spock understood, that many women from Earth would probably find aesthetically appealing.
Spock dipped his head towards the cadet, and then made his was over the snow towards the Captain. The crunch of the compressing ice crystals beneath his feel was a novel experience, and one that he was not quite sure he enjoyed. He stood behind the loosely ordered arrangement of cadets, and listened to the voice of his commanding officer.

"Right. We're going to jump straight into it, because I know that when I was a cadet many years ago," His eyes sparkled with amusement , a human emotion. "I hated long speeches. I'm assuming that it hasn't changed much, mmh?"
The crowd mumbled their assent, eager to get moving. Spock assumed they were cold. He conducted a swift check over his metabolic functions, and found himself too to be feeling the sub-zero temperatures.
"We need to walk north-east until we find a suitable spot to set our tents up. Now, as this trip is planned and were on a schedule, we can't afford to be wandering round for days, not finding stable ground. So, I know the precise location of our to-be campsite. But for effect let's just pretend I didn't tell you that. Let's get moving!"
Some of the cadets laughed at this, and followed the instructor,walking in groups of three or four. Spock waited until the last cadets had started moving, and began walking at the back of the group. He heard footsteps to the side of him, and looked down to find himself next to Cadet Uhura.
The harrowing wind beat against his coat, and chilled his sensitive ears. He was glad he had decided to wear two undershirts. Spock found himself to be slightly uncomfortable, and tried to raise his body temperature, but for some reason he had no controll over the matter. Uncharacteristically, the half Vulcan let out a small sigh of discontent; similar to the one he had heard Cadet Uhura execute on the shuttle there.
It was illogical to assume he would be able to change his metabolic rate to suite the frozen climate of his current location- his race had evolved in the sweltering heat of the desert. Spock thought of himself as part of the Vulcan race, illogically however, because he knew that his heritage was half human. He felt little connection to the loud, illogically emotional creatures that he spent most of his time around.
The rest of the walk was trying. He had began to shiver on the way, but he tried to ignore the way his lower jaw and teeth vibrated against his skull with the short muscle contractions. He leant into the relentless wind, and wrapped his arms around his chest to try to conserve body heat, but found that the gesture made no difference. The chill that had reached his bones was beyond uncomfortable: it was highly unpleasant. Yet, with this in his mind, he recalled that humans often visited climates such as these for recreation, and participated in sports on the snow. Another illogical habit, he thought. He could not understand why a being would put themselves knowingly into a position of discomfort with no logical gain.
He had voiced his confusion to his human mother when he was an adolescent, and his bemusement had grown significantly when her features had moved into a smile, and a laugh issued from her throat.
"Because it's fun!" She had replied.
To this day, even though he would not admit it to anyone else, let alone her, he still didn't entirely understand the concept. The idea that someone would partake in a pastime with no benefit physically or intellectually while another option was available that provided both was a mystery to him. Why watch a holoflim about human romantic relationships when you could choose a factual film about a historic event.
Human nature as a whole was confusing to him, and he made a mental note to study it in depth at a later date, to try and broaden his knowledge on the matter.

As the small party continued their walk, the sun grew more intense, and several of the Cadets placed a hand to their eyes to shield them from the glare of the light off the reflective ice and snow. The sun, however, did little to warm the group of instructors and cadets, to the disappointment of one member who was feeling the cold more than the others, due to his unexpected lack of control of his body temperature.
To say Spock was in-content would be a large under-exaggeration. If he was human, he would describe his current situation as miserable, very miserable. However, he was a Vulcan, so the in exact description would have to suffice. Vulcans didn't speak of emotions, and misery was an emotion. He definitely regretted signing up for this trip.
At the time, it had seemed logical. He had not experienced sub-zero temperatures before- even on Earth. He constantly migrated, and in the Winter Break, he resided in a much warmer climate, like Australia. He was so determined in his efforts of 'chasing the sun', as him mother put it, that he rarely experienced climates much colder than a crisp Autumnal day in San francisco.
"Are you OK, Commander?"
The concerned voice from beside him broke his train of thoughts. He recognised the voice, but looked down anyway to find his own eyes caught by the gaze of his partner. Apart from a slight red flush on her cheeks and ears, the Cadet seemed to be dealing with the cold well. Perhaps she often partook in illogical 'Winter Sports', so was accustomed to the freezing temperatures.
As he quickly wondered about the grounds for her inquiry, he found that his posture was hunched up against the cold, contorted into a position that, if sustained, would create negative effects on his spine. He quickly corrected his position, and straightened his spine. The second thing he realised was that his face was not his usual mask of Vulcan calm, but set into a deep frown, his eyebrows drawn in tight together, broadcasting his discomfort towards the whole party. He felt his face relax back to neutral, and he clasped his hands behind his back again.
"I am ex-xperiencing n-negative effects from the c-cold weather, C-Cadet, but apart f-from that every th-thing is a-adequate"
He stuttered out a response, giving up on trying to still the constant chatter of his teeth vibrating together. The fact that she had noticed his lapse made him uncomfortable.