Yes, most certainly horses can stress and get depressed. My gelding was kept in paddock on my parents farm. When he could no longer see the other horses (my sister's horses - we don't get along, so her horses were kept separate) he wouldn't sleep. The side effects led to low body temperature, loss of condition, hard keeper, really low immune system. Because he has AF, my vet and myself thought he was in congestive heart failure. I moved him to a pasture where he could always see his mates and he's made a 180 turnaround now that he is happy and content.
Change is inevitable, even for horses. Just make it as easy and comfortable as possible. If she has other horses around, not sure there's much more you could do to make the situation better for her. Someone else might provide some suggestions.