If you are a confident, bold rider, then I would push her through just as Toto says.
My well-seasoned trail horse is also just fine on all new trails, but as already posted, if a branch moved on the trail behind the barn, she will snort at it. Too bad for her, I don't let her sniff it or acknowledge her little spiff at all. I just keep walking, or trotting as the case may be.
I also disagree with never trotting or running your horse home. The reason that many horse want to run home is because they figure when they get there, the work is done, they'll get groomed, fed and pampered. When we get home from a ride, it's not over until I feel like its over. It might be the end of the ride right away. Or we might head out again. We might do some flat work in the yard (limited yard). I might stand in the driveway and chat to someone for 1/2 hour. I might take off the reins, put hobbles on her and work in the yard, then hop on again for a short ride. Any number of different situations. So my horse knows that coming home doesn't mean anything except it's another spot on the ride. It's also barrels of fun to come cantering into the driveway when the kids are in the yard chatting to a friend!