The question(s) that follows is what kind of bow hunting? Flat land or the mountains? Roads, trails, XC, snow or sand?
For upland game an e-bike would probably work nicely; for bigger stuff like deer probably not. Maybe with a cargo-style fat bike with a big system but "legal" e-bikes will be lacking in power.
I'm gaining some experience with a 1.9kW "plus" bike hauling trail-work tools in a BOB trailer on some fairly steep single-track and while it has plenty of power it becomes a handful maneuvering uphill when the grade approaches 20%. Hard to keep the front wheel on the ground when the trailer is loaded to the max. If I can stay on the pedals and keep my weight forward it's manageable but once I have to put a foot down (and my butt back on the seat) like on a steep and sharp climbing turn all hell breaks loose.
I guess it could haul a small dressed out deer DH or level but uphill steeps would be problematic.
I haven't taken many photos yet but on this trip I've got a gas-powered winch, 200' line, logging chain, snatch block and several slings in the trailer plus about 20 lbs on my back: