for a fast stop gap
a clean rabbit cage with a 12x12 paver in it and a milk house heater set on the paver
probably run 2 and put them on thermostats separate and probably run two extension cords to two circuits , put a weather station in the shed to monitor temp and weekly blow out each heater with compressed air, not sure how dusty a mouse house is.
keep everything clean around them.
need to keep in the habit of monitoring them regular
you get a dry heat , 2 heaters if one dies or isn't enough, keeps it where is shouldn't get knocked over or anything get too close to it
as she gets more profits from the mouse business more insulation and better heat , better electric lines run to the shed
hot water heat might be a good way to go , an electric hot water heater and a bunch of pex run under the enclosures so they stay warm and very even , a brass pump on a thermostat to circulate fill it all with antifreeze.
eventually if this gets big enough get it on the OWB as it's own loop
just thoughts
I was thinking about hooking it up to the owb but like everything it's getting more involved than i have time for now. I do like your stop gaps.
Now I'm going to be lucky to get it insulated celling in and flooring down before temps stay down. Another thing I saw on line were electric heaters that mount overhead and should greatly reduce the chanc of getting knocked over. down side is the floor will be cold.