How can we stop frost from forming on the inside face of the garage walls?

This sounds like a classic case of indoor air leakage. As warm, moist heated air from inside your home escapes into the garagespace during winter, it condenses on the coldest surface around. This is the only possible source of moisture in this case, and it makes sense that your exterior garage walls would be hardest hit.

As for a fix…

• Start by making sure that the door from your house into the garage is perfectly sealed. Treat it like any other exterior door.
• Next, look carefully for other areas where air from your home could be migrating into the garage.
• And of course, any exhaust fan vents that might have been mistakenly directed into the garage would have to be redirected outdoors.

Even if you try to eliminate warm air migration into the garage, some will invariably occur as people move in and out of the house. That’s why you’ll also want to boost garage ventilation. Keep a window open a bit whenever there’s no blowing snow or rain to give the moisture a chance to escape.