I'm wondering if anybody uses compression fit long-sleeve shirts to keep their arms warm, how different are arm warmers with regards to the fabric.

arm warmers are the same thing as the compression type stuff. Usually they are a little thicker as they add a bit of a light knapp to the back to increase warmth as they are for cold weather. The underarmor type shirts can be had in light and heavy as well.

They'd feel the same but the arm warmers give you the option of peeling them off and tucking them away once your body heats up or you hit the big hills and need to stay cool. I tried some arm warmers once instead of getting dedicated cold weather gear and it was sort oif annoying to me due to the fit. I don't use them and opt for a light jacket/vest shell instead.
I do like the knee warmers though as my knees feel creaky and cold in low temps. There is little fat or skin insulation to protect them.

I dislike those "compression" shirts. They never really feel comfortable to me.

I'd like to find cheaper white long sleeves in a very thin material for riding to keep the sun off my arms. I hate the feel of sunscreen but can't survive without it.

Unless the fabric has a rated SPF, it isn't going to keep the UV off of you.

Wally World has them real cheap here in Canada in all different types, long sleeve, T-shirt, sleeveless. They can be found in the mens underwear/pyjama section all for around $12 each. Nothing in white though.