L.H.
activities for a one year old can be fairly simple, yet very stimulating.
IE: squeezing glue on a piece of paper then sticking various 'trash' household items to the paper (toilet paper rolls, glitter (dirt/sand/leaves/sticks if you want to just use 'earthy' outdoor things), buttons (if you have extras of those things) paper clips, etc...just random things you find in the house...and then you can chit chat about what those items are normally used for and how he/she is making art with them.
maybe next winter you can order some of those pre-organized crafts for kids...I think http://www.mothergoosetime.com/ is one site that sells kits.
Good Luck :)
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I just remembered a VERY FUN activity we did indoors one day and the fun lasted for a LONG TIME.
"INDOOR WATER PLAY"
I filled a few pitcher fulls (not a lot really, maybe an inch or two deep) of warm-ish water into a blow up boat (didn't have a kiddy pool handy) and lined the living room with towels...he was having a nakie fun time running all over jumping into the boat full of water splashing.
Here is a link to a photo of him having a great time. :)
http://i59.photobucket.com/albums/g293/Hinnrichs/IndoorWa...