There is a way for you to trade between Gameboy Colour and Advanced, but it requires a special cable.
Those cables won't be sold in any large shops, so you will need to get one second hand. It's more trouble than it's worth, really.
No , it is impossible. GameFreak made it so you cannot trade between Gen 1-2 (Gameboy Color) and the later games. Furthermore, you cannot trade at all between those consoles since there isn't a cable for it.
EDIT: As marzipan pointed out, there seems to be a cable to trade with.... But despite this, you cannot trade between Gen 1/2 and Gen 3/4/5.