Could you possible rent the house in England and just rent an apartment or small house in the US?
In reality, it does not snow very much in Anchorage compared to other regions of Alaska, and when it does it does not take long for it to melt. The fluffy and big snow flakes provide you with great opportunities for taking beautiful landscape photos, and it's usually not very cold. I would not worry whatsoever about being buried in snow and having to dig yourselves out
Every now and then the streets in Anchorage get very slippery, and driving conditions become hazardous. But once you have enough practice driving on icy roads, it becomes much easier. All I can tell you at the moment is that Elmendorf is a very popular location with military members. The roads leading out of Anchorage (Turnagain Arms, and such) are very scenic.