What are the possible ways to prevent heating pipes in an entryway from freezing?
Some different ideas:


Remove the baseboard water heater and replace with electric, thereby creating it's own zone. If the only pipes in this room were for the radiator, you wouldn't even need to set the heat, as there are no more pipes to worry about.  
Add insulation to the mudroom
Keep mudroom door open when using wood heater
Splice your pipes and add the mudroom baseboard to one of the other circuits that will be running even when wood stove is on (basement, likely).