A friend who had a child almost a year before me gave me really good advice: leave one drawer in the kitchen full of plastic containers, spoons, etc. that you're OK having them get into and play with - even if it makes a mess. You can teach them that is their drawer, and they can play with whatever is in it.
We never child proofed our house other than a tension gate at the bottom and top of the stairs, rubber bands around cabinets we didn't want them getting into (such as those with kitchen chemicals), and safety locks on the doors to the bathrooms, basement and garage.
Have you considered getting a cheap stool (if he likes to climb) that is low to the ground and lets him get his climbing interests out of the way? Sure, he may occasionally fall, but I'd rather my kid fall 6 inches than off a chair.
Winter is a tough time for having a little one who's mobile. We play smash and crash a lot to get their energy out. Pile up a bunch of pillows in a hallway, let them run, knock them over, and do it again. It's cheap entertainment that burns off a lot of pent-up energy and helps you keep your sanity.