I think it depends on the horse. We moved our horse about 3 weeks ago and she is now alone. Well, almost alone - the neighbors have 2 horses that she can visit with over the fence. I was very worried about her "loneliness" but it hasn't been an issue at all for her. She is relaxed and seems very happy. (Even more than when she was with her 2 stable mates - I'm still a bit shocked!) Sometimes the neighbor's take their horses trail riding for the day but Lily couldn't care less. A week or so ago I was on my way to see her and I saw the neighbors pulling into their driveway with their horse trailer. I was thinking I wouldn't be able to ride because she is probably dripping with sweat from running the fence and yelling for her buddies. Not the case. We got to the barn the same time as the neighbors and they were putting their horses in the pasture. Lily was cool and calm. The horses came running to the fence and whinnying for Lily. Lily looked at them like "yeah, I see you but my people are here so we'll catch up another time" and whinned to us in return! She would rather see us and wasn't bothered a bit by being alone.
Like I said - I think it all depends on the horse. Lily is an Arabian and she is a total people horse. I now believe that she prefers people to other horses. She has made this move beautifully. One thing we have done to help her with the transition is to spend a lot of time with her. We have been very committed to that. The first few days we scheduled time for her - like 4-6 hours a day!! We have had picnics next to her paddock, read books next to her stall, lots of hand grazing, ground work, grooming, riding, etc.. It sure has made all the difference in the world!
Best of luck to you!