I don't know where you would leave your boots, unless you can fit them in a bag or purse. During your interview you will leave your coat and belongings in the office where you check in, but there's not a ton of space and I wouldn't bring boots to leave on the floor in there. There's a coat rack for your other things. The sidewalks around the school are kept fairly clear, so unless you want to hike around campus (not necessary - the CVM is all in one place!) you won't need boots.
Thermals shouldn't be necessary - you'll be inside for the majority of the day. If you have a sweater or jacket that you're wearing to your interview, that should be perfectly fine. Some parts of the school are a little chilly, but nothing too extreme.