All fixed mount satellite antennas will be affected by trees and weather. Sometimes you can move the RV a bit to get a clear line of sight to the satellite, sometimes you have to change sites.
The dome style antennas, having a smaller effective collecting area, are more subject to weather dropouts than the larger, circular or ellipitcal dishes. Some owners have complained about moisture from rain or dew also degrading the signal.
However, if you want inmotion TV, then only the dome antennas will work.
The dealer had trouble getting our King Dome to work when we bought the coach new. They changed the dome and told me it was OK, but it still didn't work. They called King Dome who told them to change the cable. It then worked, but I'm not convinced it wasn't just a bad/loose connection where the cable plugs into the dome. Simple to check - just unplug it and plug it back in again.
We have a Kingdome (stationary) and it has worked very well for us, we've even received reception as far north as Nova Scotia and Prince Edward Island. No it won't pull in a signal when you are parked under a tree, direction of the RV position doesn't matter as long as there is a clear view from the satellite to the antenna, usually to the SSW. We've had some dropouts under very heavy rainstorms and real heavy morning dew. I just wiped down the dome with a Kingdome product that improves reception in the rain, it seems to work but is hard to tell.
Any dome antenna will be affected by moisture. Weather and trees are always a problem and an enclosed dome is more affected than one that is not enclosed. If you plan on spending most of your time in the Southwest then a dome will probably work very well most of the time.
One thing you can do with the king dome to improve it's light rain performance (NOTHING works in a heavy rain) is wax it with king-dome anti-rain-fade wax which you can get at any place that sells king domes. Works on other domes too
Likely should be done a couple of times a year
I'm still waiting for the rooftop antenna with the high powered tree cutting laser option so you can actually SEE the sky