I too would really limit the amount of TV you let him watch. I have friends with kids that cannot entertain themselves becauce they are used to constantly being entertained.
My boys are 6 and 2 and believe me, I too know what it is like with a toddler in the winter. Here are some things that my sons like:
Child-sized cleaning supplies (ex. broom, dustpan, rags, vacuum cleaner) they love to imitate anything you do.
The good ole pots and pans and don't forget the wooden spoons.
Glue sticks, paper, cotton balls, stickers, dot paints. Make simple things. Snowmen, cards for grandma, trace his hands and feet. Cut and glue pictures out of magazines. Staple pages together and make a book of animals, people, or toys. Then share it with daddy.
Blow bubbles inside. If you are worried about the floor, lay down an old blanket or towel.
Put snow in a large plastic bin and bring it inside for him to play with. HE WILL LOVE IT! Again, cover the floor if you are worried.
Another day, fill the bin with rice and let him play in it like it is sand. Use cups, trucks, animals, etc. This is easy to sweep or vacuum up. (and safe for him in case he puts some in his mouth.)
Let him help you "cook." Instant pudding anyone? He can pour and stir, even help you slice bananas with a plastic knife. Then of course, EAT!
Go to the library and read, read, read to him. Many libraries have toddler story times with songs and simple crafts. Of course he won't sit and listen to the stories right away, but keep taking him and he will learn.
Teach him simple songs and fingerplays. Ring around the rosie, pat a cake, this is the church.
Check out meetup.com to see of there are any moms groups in your area that you can get together with.
These are just some of the ideas I could think of off of the top of my head. Most of them don't cost anything. You are your child's first teacher and he will learn so much from you. You will be so proud of him (and yourself) when you see him learning.
Good luck and have fun.