We're dealing with this too this year with our 3 1/2 y.o. He didn't notice Christmas last year, but he sure does this year.
We do many of the things that others have posted - read Hanukkah books every night (we start doing this right after Thanksgiving), play dreidel, having friends over to play dreidel, do Hanukkah crafts (stickers, stamping), went to a big Hanukkah party at our synagogue, and will be having 2 family Hanukkah parties this weekend.
We talk a lot about being Jewish, and DS tells people "we're Jewish, we don't celebrate Christmas" or "we're Jewish, we celebrate Hanukkah", but we do live in a highly Christian community, and there are lights and decorations everywhere, and everywhere we go in town people want to talk to him about Christmas & Santa. I usually nip the conversation in the bud.
But he does love looking at all the lights (who wouldn't?) and he waves and says hi to all the plastic santas he sees from the car. And he loves Christmas music (which we try to avoid, but they sing at preschool).
When DH was little, his teachers told him there was no santa but he had to keep the secret form the other kids. Personally, I feel like that might be a little bit too much responsibility to put on a 3 y.o.
I grew up in a Catholic household, so I've spent many years getting over "losing" Christmas. We're committed to raising our kids Jewish, so there are no dual celebrations in our household. We typically go away for Christmas Eve and Christmas day - to a hotel somewhere nice with a pool & jacuzzi

but funds were spent on another vacation this year - so it will be rental movies & jammie day for us on Dec. 25 this year!