Yes, they will rent to you as a member of the community. Here are their rates. It's still a good deal. You could ask if they will honor your student status (even though you are at UofI), won't hurt to ask.
Follow the advice above about waiting until Spring, or better yet, to tackle bigger peaks, especially if you are going by yourself. My advice is to sign up for some trips through U of I's outdoor center when you head back to school and that will expose you to some more adventurous places and activities, sometimes. School sponsored trips tend to be small, full of expert advice and it is a great way to go places and do things on a budget (you are a student, right?).
Good luck, be safe, and have fun. As someone who always takes off alone, try not to go alone. Seriously, especially in the winter.