Just to manage expectations:
Most of that snow looked closer to ankle deep than knee deep to me. But if you look closely, you will see that the actual walking paths were completely clear.
The university has seen a snowfall or two, and it’s pretty good at dealing with it. At a certain level.
Usually as a student you will not be deliberately walking into the uncleared part to have a snowball fight, you will be walking on a cleared path.
However that path may well have a layer of snow,slush, even ice still lingering.
Moreover, walking on sidewalks, and especially crossing streets, you will encounter much slush. For long stretches of time. Particularly as you walk off the campus proper and into Collegetown, for example.
If there’s a point to this, I guess it would be that you should certainly have some sort of waterproof/resistant footwear, with gripping/ rubber treads, extending at least ankle length, but it does not necessarily need to extend all the way to your knees.
Also, I just looked it up, at the time of that snowball fight it was about 30 degrees out.
Which is historically a very representative high temperature for a day in February; a little on the low side actually,
It does get a lot colder, though, on the odd day (and every morning & evenng), and sadly last winter that odd day wasn’t so odd. Hopefully you won’t soon have a repeat. But, on those days, additional layers can be your friend,
Interestingly, I did not make the acquaintance of thermal underwear during my time in Ithaca, That came later, when I lived in Chicago. You may need it sooner than I did. Then again you might not,