The sad truth of the matter is that honest AC people are scarce. Seems sometimes that most of them will come out and then try and sell you a new unit rather than mess with the old one. But, having said that, if you check with neighbors or friends a couple of names that they trust should rise to the surface.
Another good source of referrals is your local electrical supply house. The men and women who work at these locations sell parts and supplies to the area professionals and they know who is good, not so good or a crook.
The typical tune up should fall somewhere between $50 and $100 with higher levels in the event they find something amiss. Depending on the kind and age of your heating system you should have it checked at least every few years or so to save yourself the headache of a failure right in the middle of a blizzard.
But, let’s say you do have a problem and its near zero outside. First thing, don’t panic. You can always retreat to a friend’s house or even a motel for the duration of the cold spell. At that point you will be in emergency mode and will not have time to vet the local furnace repairman before calling him to come fix the old heater. Just be prepared to get soaked.
Second best would be to have secured the phone numbers of a couple of recommended repairmen and to have their numbers posted right next to the furnace. It should be someone who lives close and better yet, a repairman that you or a neighbor has a history of using. Make the call then all you have to do is try and stay warm while you wait for them to arrive.
You did buy yourself a space heater, right? Make sure you have at least one or better yet, two or three around to take to the most insulated room in your house. Close the door, turn the heaters on and you’ll be nice and cozy. Second best would be to have an auxiliary heat source like a fireplace or pellet stove that you can use to heat your home. Either way, heat only the minimum space you need to and make sure to wear layered clothing that can the added to or removed from your body as needed. I wouldn’t worry too much about the pipes freezing unless it is really cold outside and or the repairs will be some days in coming. In that case, open the faucets in the kitchen and bathroom just enough to let the water drip. That will help prevent the water from freezing in the pipes should they drop below 32F.