Unless you are going to a very high resort, and taking your baby right to the top, I genuinely can't see altitude as a risk. Given the number of companies that are set up for skiing with babies/children these days, I would have thought someone would have looked into it by now, and I have never heard even any anecdotes of babies having problems.
We took a BabyBjorn type thing, didn't bother with a buggy. He was much happier being carried anyway, and there would have been too much snow in resort. By end of March though, it might well have all gone at that level.
The hotel we were in was fully set up for babies so had sterilisers etc there, although I was still BF, but it meant I could clean my pump etc (expressing on a mountain side halfway through a day's skiing, now there's another story...) If you are not in a hotel and need to sterilise, you might want to get some of the travel steriliser bags, either cold water ones, or microwave ones.
I got a pair of those BabyBans sunglass things, but he wouldn't keep them on (they are now used as 'goggles' in the bath). We borrowed a really snuggly snowsuit. At that age though, he wasn't really outside all that much. The following year, with a toddler was far more challenging, and we've not made it back again the last couple of years with pregnancy no.2 and baby no.2 and a DH who keeps disappearing overseas etc....
We did go so that we could ski, so DS was in creche during the day [bad mummy], and it was the first time he had been left. TBH, he was so young, he didn't know any different [really bad mummy]