I don't hunt, but I do use boots! From what I've seen, boots that fit really well won't come off, but if they're even slightly too big they'll come off exactly when you really wish they wouldn't. I've galloped xc in mine, gone down plenty of roads, crossed lots of water, gone through knee deep mud (yes, it really was kneed deep), and trotted/cantered in all sorts of gross, muddy footing. I've yet to lose a boot.
I ride my horse in Old Macs, I use them when I'm going to a place I've never been (and don't know the footing) or know that I'll be riding on gravel roads/rocky footing a lot. Longest ride in boots was about 6 hours, going through water, mud, roads, etc. Plenty of cantering/galloping. His boots were fine.