Should a Stone Home be Insulated or Allowed to Breathe?

Hello. I have purchased an almost 200 year old stone home in Canada. The exterior walls have been repointed and are looking gorgeous, although I do not know if the repointing was with a lime-based mortar or with cement. I'm praying it is the former. On the inside of those stone walls, a couple of walls were insulated with fiberglass batts and covered with drywall. Other than mice, there's no evidence of moisture or damage. Other exterior walls are done with lath and plaster. Again no evidence of any problems, although those walls are quite cold. My contractor would like to build false walls and insulate. In the best of all worlds, he would prefer spray foam insulation since it gives an airtight seal, but he is also fine with new fiberglass batts. I've read a number of articles, many of them from the UK, saying that I should not be insulating stone - that I affect the breathability of the house. My contractor says but the winters in Canada are much colder than those in the UK so the comparison doesn't work. I'm making it sound as if the contractor and I are at loggerheads which isn't the case. He has worked on a number of stone homes in my neighbourhood as have many other contractors who also insulate the stone. I just want to make sure that any decision I make now isn't going to come back and bite me in 15 years. We're gutting the house so now is the time to get it right. Should I be insulating and, if so, what's the best method? Any expert advice you can give in that regard is so appreciated. Thank you.