This could be so many things. Many of the things should be checked out by someone that knows there way around these small furnaces as a propane explosion is not a good thing.
One thing you can do is to examine the line supplying the furnace all the way back where it hooks into the main truck line back to the regulator at the tank. Are there any kinks or major dents?These would restrict gas flow and these points may internally freeze up or constrict in cold weather.
Bear in mind that your furnace needs more gas than your stove and probably your water heater. If your regulator is defective your Furnace may not have enough pressure for the safeties to allow it to light. You can measure this gas pressure but it is only about 10" of water column(NOT PSI) so it is better to get someone with a gauge device that is made for it. The gas pressure in your tank goes down with temperature so the regulator would need to compensate.