First of all, welcome to EE.
Regarding your problem, I think you'll be lucky if you manage to get a fix at all. Also, I am pretty sure this won't be achievable with one of those \$2cm^2\$ patch antennae that are widely available, you'll need a) a big patch antenna, or b) some more complicated dipole/loop antenna goodness.
Anyway, I would strongly suggest getting to the forest (or any forest nearby) with several GPS devices and see what you can get out of them. You'll likely get into trouble getting a fix, but I'd give it a try.
About your Differential GPS idea - do you think your copter will have comms with a nearby-standing ground station? If you can guarantee this, then it might also be a way to go.
You could take this a step further: have two (or more) stations whose location you know and triangulate your flyer's position based solely on your "D-GPS" system, without getting a satellite fix onboard, at all. That would require some lower-frequency radio to dig through the wood, but overall, might be more stable/consistent.
No more ideas, sorry if I misunderstood your question.
Cheers. [1]: http://files.microstrain.com/TN-I0028-GPS-Antenna-Performance-Comparison.pdf [2]: http://avrproject.ru/EB-500/GPS_Antennas_ApplicationNote-GPS-X-08014-.pdf
