I have two questions, can I trap crawdads in frozen lakes?? And do you know of any effective somewhat simple homemade traps?
Any tips would be greatly appreciated.

I trap them in the summer with a conventional crawfish trap. I have seen them through the ice along the bottom in the winter in the shallow water but not often. I don't know if anyone does trap them in winter. Let us know if you do and it works out. The trap I use in the summer is cheap and available through many of the sporting shops or bait shops in the area. They crawl up the ramp and fall into the holding pen where they can't get out. When I really want to catch a bunch I seine them with a 6' net with poles attached in some of the small farm ponds. They are usually soft shell and great for bass bait. 3 or 4 good scoops and I can get a hundred. Just lower the poles stretching them out as far to the sides as you can bringing the net down near the bottom and start to walk. When you get near the shore lift the poles and the net is usually full. Works in small rivers too.

I don't know about frozen lakes but hot dog wieners best ever bate for catching crawfish!