So, some ideas:
there are washable markers and crayons and finger paint that comes off pretty easy when it strays from the paper. If you don't notice it right away, it can need a little baking soda to help it off, but that is all.
Our DS REALLY loves to:
help me cook- usually I let him pour the stuff in, sometimes he holds a knife handle while I chop, he likes to stir... sometimes I give him his own flour/water or beans/rice etc to mess with- he sits on the counter by me while we do this
finger paint- we give him the paint in smaller squeeze containers and let him go to work- this entertains him for LONG times
pour beans/lentils/rice into different containers
play with water in its many different forms
listen to music/change music/dance to music
roll around the house on a radioflyer (kind of like a trike with no wheels)
play with boxes (climb in and out, stack, put toys into)
play with rocks we have in planters around the house (move from one to the other, put in boxes, put in potties, carry in his chin, or push around on the radioflyer)
water the plants
clean the bathroom! (important to use non-toxic cleaners! mostly vinegar spray bottle, baking soda in a powder bottle)
read books- not just kids books but also books from the clearance section of the adults area with good pics- art books, fish id books, animals books, coffee table type books you can get for cheap
copy how we skip- i copy him, he copies me, etc for some reason this is a big giggle time
In general we try to play with him, but not for him: play that is just you entertaining him is the least use to her, and just a replacement for the TV. Play that is about learning what we do (cleaning, cooking, building, making stuff to sell, dancing, etc) is both learning and playing, not just entertaining/passing the time. Play that is connection for the two of you is never boring to either of you and makes the whole at home with a toddler life pretty fun.
"That's the way it is, if that's the way it seems to you."
"Cosi e se vi pare."
what i noticed at 2 is all the crafts are meant for older kids. colouring and everything because it all stems from the wrist movement.
so what i did was find a tabletop on trash day out. 6ft by 3 ft. i got newsprinter uber cheap from our local newspaper. i set the table top up carefully and that became our easel and dd with her butterfly wings on could use a bunch of mediums to paint. sponges, brushes, her fingers, a piece of cloth. she loved that. and never ever has painted on the walls or door or anywhere.
i would put newsprint down and cover the floor (no carpet) and dd would paint with her feet. the more messy the more she loved it.
dd was never into toys or puzzles or craft. she loved my tupperwear drawer. rocks, stones, sticks.
the tv was for me. we'd do tv once in a while. meaning dvds. so it was never really a problem.
looking back i dont know how we passed the time, but somehow during winter we always found something to do at home. do u have a map? map was in fact one of dd's first words. we spent a lot of time in front of the map.