Most of the time if you look for movies that are based on true stories, you won't get those sticky-sweet, cheesy movies like lassie. Seabiscuit was one of the best, along with Ruffian (though that one was terribly sad). Hidalgo was a good movie for entertainment value but I wonder about the "based on a true story" part of it. My favorite movies of all time were probably the Snowy River movies. That is why I love black horses now. I still get chills when he tops the hill for the first time at a dead run on the black horse (in slo-mo no less
). Though Second Chances is more of a kid's movie, I still enjoyed it and Wild Hearts Can't Be Broken was great. Black Beauty is a classic that isn't terribly touchy-feely.
Whatever you do, avoid Casey's Shadow. That was one of the worst movies I have ever seen (and I have seen some doosies).