Have no idea what furnace Jayco uses.
The furnace should have a data sheet. Typically in the owner's manual. If not inside one of the covers. What I want to see is the wattage.
Are you really planning on having the blower run for a full 8 hours at night? Usually they only cycle on when heat is called for.
The battery capacity will get you through the night. The solar needs to be sized to replenish the battery and possibly run the heater during the day. So once we know how much the blower will pull out of a battery, we can size a battery that will work and tell what solar will work.
Does the 160W panel have the potential to do the job? I think so. If the furnace isn't running too much, if it isn't too much of a power hog, if you have good sun during the day on the panel, and about 20 other variables...
If you can't find the specs on the furnace, it can be measured. There are a ton of low cost 12V watt meters on places like Amazon. Put it in line with the battery, run everything as you would for a night but for a hour. This will account for any other draws that may be in the system. If the furnace runs for 15 minutes out of an hour, run it for 15 minutes in that test hour. Subtract the watthour reading at the start of the test from the end of the test, that is how many watts you need to plan for. I would recommend rounding up in case you get an extra cold night or the solar doesn't get enough sun.
How many nights in a row? You might be better off with a little extra battery and letting the solar charge on the weekdays that you are not in it.