Actually you need fast shoes to keep ahead of the moose
Moose are not common but when I see one I give them wide berth. I was in Alaska last summer and all the runners there are more worried about moose than bears. I actually almost ran into one, early one foggy morning near downtown Anchorage. In my neighborhood, hmmm, also coyotes - nothing to be concerned about, large herds of cows that escaped from somebodies pasture and follow you around, the occasional mountain lion (despite no mtns), various weasels, jackrabbits, crazy kids in old pickups, and worst of all, the skunks! Especially at night. They move slowly, are not inclined to get off the trail (but it is so much easier walking on the trail than through the tall grass, plus we get to make large bipeds change course). Other than that, it is pretty tame here. No bears. I did some snowshoe running in northern Minnesota a month ago and saw lots of wolf tracks, but did not see their makers. I often run (canicross style) with one of our dogs, if it is not too hot, and if they see something furry, it will be a wild ride.