RE: hot water heater. You said "valve" not switch. Where to find the valves.
Access to the "winterizing valves" for your hot water heater will be inside the rig...directly behind the hot water heater. The heater is typically mounted in the exterior wall where the heater itself can live in the cavity created by a dinette bench seat or similar. It could be under your bed. Less likely, it's in the back of a cabinet hidden by a protective panel that comes off with 4 screws.
Whatever is directly inside the rig behind the hot water heater as viewed from the outside is where the main body of the hot water heater lives. And that's where the valves are. You might need a screwdriver to remove a screw holding a plywood cover over the heater. In two consecutive campers, mine has always been in the dinette booth seat.
Furnace: typically the furnace responds entirely to the thermostat. No master switch. There is usually a slide switch on the thermostat for "on/off". Then you set the thermostat to "demand" heat. If it's 75 degrees in the cabin, you'll need to set the thermostat to 80 degrees or more to force it to start.
While the body of the furnace proper may have a switch on it, that's usually buried inside the cabinet that houses the furnace, so you have no access to that switch.
If your thermostat makes "something" happen...some furnace noise in response to the call for heat, then the thermostat is probably no the culprit. I the thermostate makes NOTHING happen, remove the thermostat from the wall (cover snaps off then 2 small screws) and check the wires to the thermostat. Just two wires for heat. Chances are your air conditioner is not controlled by the thermostat, but if it is, there will be 4 wires. Two for heat and two for cool. Easy. Do yourself a favor and
replace the thermostat with something from this century. My 2020 rig came thru with a mechanical antique and I ditched it right away for the one in the link. Nothing special about mine...shop around. THEY ALL WORK THE SAME. On/off/On switch for heat/off/AC. I don't have thermostatically controlled AC in my rig or in my home. That thermostat, with just two wires, controls my furnace at home and in the RV. Couldn't be easier. Whether this fixes your problem or not, you'll be happy you made the swap.
Now...if you know the stuff about the thermostat already, you might be experiencing a problem with your furnace. There are several problems, but I'll mention a likely one. The "
Sail Switch". Symptoms of a problem sail switch. You call for heat with the thermostat, the blower fan starts and runs for 15 or so seconds, you might or might not hear other clicks and noises (usually not), then the furnace shuts down. You must turn the thermostat off then on again to get it to try again. Usually no miracles happen. Your sail switch may be dead or dirty. Depending on your DIY skills, a sail switch replacement is pretty easy. If you can't deal with the sail switch, the other possible problems (control board, gas valve, etc.) are harder still. You can call a mobile RV repair to deal with the furnace if the thermostat doesn't perform magic.
Mystery switch: My rig has a light under the stairs outside. The switch for my light is similarly located...down low, near the steps into/out of the rig. A 2003 rig most likely has all incandescent bulbs, and a 22 year old bulb might be burned out. If my hunch is right, look for a fixture of some sort under your stairs. See if you can remove the lens over the light fixture, remove the incandescent bulb and replace it...or better yet,
get the number off the dead bulb and find an LED bulb replacement. While you're at it, upgrade all the bulbs in your rig with aftermarket LED replacements and/or replace aging fixtures with LED fixtures. Your eyes will thank you, and so will your battery. If this switch does control an outside "stairs" light, FYI, mine is "blue" and not all that bright. It's just meant to light up the steps when it's dark, but it's a pretty low wattage bulb. If you replace the whole fixture (presuming you want this feature),
you'll probably want something that puts out low lumens for a simple reason. This light is very easy to forget to turn off...out of sight out of mind. Very often you'll forget to turn it off and leave it on all night...annoying neighbors and draining your battery if you are boondocking. Ask me how I know.
Of course, these are all shots in the dark. My solutions may not fit your problems.
Good luck.