We have a well and well house also. ..here in central Virginia. ..we have flood light in the well house....we also have a small electric heater that we can plug in if we have brutal weather...our well house is a block building with pitched roof....the original 36" bricked well is also in it along with our bladder and other well stuff...Beginning day 3 with no water. We have our own well and the problem seems to be at the well head or in the well house in spite of having heat lamps on everything. It's supposed to get into the upper 20's today. Although that is not quite up to the freezing point, maybe it will help some as long as the sun stays out. Back to the old timey ways of heating stored water to wash everything.
We were in the single digits for many hours so dh plugged up the little heater and set it to cut on and off and to keep the well house warm..our well house did not freeze....we moved into this house back in 1999..it was built in the late 1800s and had no water in the original part of the house....they added a back section in the 1920s....all the water is in that section and over the years we have had frozen pipes and broken pipes in all the possible places and I have heated water like you are dealing with and boy it is no fun...we found that it was worth putting a bit money into the well house and even insulation if need be to keep it warm...we also have had frozen pipes under the kitchen many times...we replaced the copper pipes with pec....which is more forgiving if frozen..we have both heat tape (we keep several heat tape on hand as spares because they can go bad) and a trouble light with a rough duty bulb..which we plug in if brutal is coming..... these are just things that we have learned over the years...maybe there is something there that you can use to help you to keep this from happening in the future. ...it took us years to get it all figured out....