DIY ideas to insulate a hot tub pump

Got a lazyspa hot tub but instructions say pump should not be left outside if the temperature drops below 4 degrees. However I love having the hot tub out when it’s cold and snowy as that’s when it’s the most fun to use. Plus where I am it can be very unpredictable temperature wise so it might be 6-10 degrees all week then I go away for work for 4 days and the temperature plummets...

So I was thinking of trying to build a little wooden hut/housing/box with a lid and lots of boiler lagging or something similar around the pump. Has anyone done this before or something like this? Could it make the pump overheat if it isn’t that cold? Any ideas or examples? I haven’t found anything on the internet yet...