What to do about trees in neighbor's property?

Hi everyone! I'm looking for advice here. I live in New York and invest in Jacksonville, Florida. I have a single family property there. My property does not have any trees on it but the surrounding neighbors have huge trees that go over my house and over the yard. I am a nature lover, I do NOT want the trees cut down at all, but what do I do in this situation? Can I ask the neighbors if they will trim some of the branches? How do I ask them if I live 1,000 miles away and am never in the area? Is this a normal thing to ask? I don't even know if I'm allowed to trim them myself since they are not my trees. Hurricane season is approaching and if those branches go flying, it would definitely damage my old roof. Any advice would be appreciated. Thanks in advance!! 

You can see the trees in the listing here: Zillow listing of property