Grrr...
Alchemize cloak with robe.
While you did think it would solve your chair problem, you don't have anything else to cold-proof yourself with, which is necessary for a Cryomancer to have. You sit on your bed and try to remember anything about making clothes cold-proof.
A few hours later (and one or two secretly 'borrowed' winter cloaks from those at the tower bottom), you have a horribly combined, but good enough, cold-proof blanket. you cover your awesome chair with it and sit in it. still slightly chilly, but you're a Cryomancer-in-training, might as well get used to it.
Find a town full of children and offer to make it snow in exchange for their allowance. Find enough kids and that will really add up!
Sitting in such a grand chair reminds you of your lack of money.
One freak snowstorm could easily be explained away, its not fully spring yet, so you go up to the town park, and tell one of the kids your plan, making sure he remembers not to tell the adults. You ask him the next day (or one that looks pretty close, the town kids aren't that different to you) and he tells you they have 12 gold all together, though it'll all be in silver pieces with a few coppers. Good enough. You tell them to wait patiently until next monday (3 days from now), and he takes a smallish bag out of his backpack and drops on the ground in front you.
But what to do with the time until then?