If you let the clay set in the fridge for a bit it will stiffen up. I had to do that since clay acts different up here in the mountains compared to where I used to live. I had to work with the clay a bit, pop it in the fridge for a while, then work with the clay again....it was a continuous cycle. lol
I'm not sure about the Apoxie Sculpt brand, but my husband used green stuff (basically a type of apoxie that the Games Workshop company sells to it's gamers) and it handled the oven just fine when I baked it at 200-215 F. It didn't seem to droop, melt, get soft or brittle, or anything.
I've never tested baking a painted pony, but I have heard that the paint can bubble up. I've always baked then painted.
After baking the plastic on the pony will be VERY soft, try not to touch it until it has cooled down or you might run the risk of the clay separating from the plastic. The plastic will bend and the clay won't.