Thanks for all of the replies!
I crawled up into the attic and found that the antenna is a General Electric 24802 (
http://www.amazon.com/GE-24802-Anten...keywords=24802).
rabbit73, Jake V, it's mounted facing north, and I'm more interested in the stations to the north. The roof is plain sheathing and asphalt shingles, no metal mesh or lathe that I know of, and the antenna is up against it, so I don't think siding will be an issue. I agree that the powered splitter and powered antenna combo are not the best choice, but I though that the antenna would have a weak amplifier and when combined with the long cable run to the basement it wouldn't hurt anything.
Attached is a picture of one of the trees. All three are very similar, being mature maples > 50' high.
I attached the antenna directly to one of the TVs when I was testing the feasibility of this idea last year - I seem to remember getting good reception on everything. This was in December, though, after all of the leaves had fallen. I'll try and get back into the attic with a cable to test it again.
Thanks again for all of the help!