In early December while we were on vacation our heater shut off and subsequently pipes froze causing water damage. What are some reasons the furnace would stop working?

More than we can count on our fingers and toes.

The easy thing to check: Look for any burnt wires. If you find them, replace them and see if that solves the problem.

Also, try your thermostat settings:
Will it run on fan only?
Does the A/C work (if you have it)?

If it's gas, do you have a pilot... and if so, is it lit?

What kind of system do you have?

If you didn't find and fix any problems with the furnace, I would look at a flaky control board or thermostat. Depending on how old it is, there are a number of things that can go wrong, pilot light out, fuse blown in the transformer circuit, bad temperature sensor, blower problems, etc. None of those will go away itself.

I would keep an eye on it. An intermittent problem is likely to come back. You are unlikely to get frozen pipes the balance of this heating season or early the next. It would be cheaper to replace some of the likely parts including the circuit board, temperature sensors, and the ignitor before leaving the house empty in severe weather again. I would give things as much chance to go bad as I could, before throwing parts at it.

Thanks. The furnace has been started again and seems to be working now. Was wondering if condensation could have built up or other circumstances could have caused it to go out when the temp got so cold. Again thanks for the feedback.

If it is a 90+gas furnace condensation may have been an issue if your condensate pump is wired into your thermostat lines and the line froze it may have shut it off... without knowing your fuel type oil/gas/etc its hard to throw u some suggestions because there are so many if ud like more info tell us the specifics of your system and ill throw u some suggestions or things to keep an eye on