Tall Boots (defined as boots that reach to the knee or above the knee) can be worn with long or short skirts. Do be careful when wearing any skirt that is over an inch above the knee. Coupled with tall boots, this can be very streetwalker-ish. Anything to the knee or below is appropriate and stylish. Ideally, you're wanting to cover your leg (because it's cold!) but if a little of the knee is showing, it's fine.
Medium Boots (defined reaching anywhere above the ankle and below the top of the calf) can be worn with both long and short skirts. Same caution with super-short skirts as before and a note to avoid the horrid Ugg boots with mini-skirt trend.
Tights are almost always appropriate and even encouraged as the weather gets cooler. These can be worn with all boots and skirts but are encouraged if you'll be showing a lot of leg. Go with an opaque or semi-opaque pair and maybe try different patterns.
Fabric: I'd stay away from overly summer fabrics with boots. Since boots are usually of a heavier material, you want to sort of "match" that with your skirt. Tweed, corduroy, denim, heavy cotton/linen blend and knits are appropriate. I'd pass on lighter cottons, rayon, jersey or cotton-poly blends.