I'm no expert but here is my experience.
the expansion of the liquid into a gas inherently requires heat (evaporation is a cooling process) which is why the tanks chill when they are being used. most of the smaller 1lb tanks ice up because you are removing the propane at a high rate (compared to the volume) which means quite a bit of heat is required to maintain the remaining lp as a liquid. The larger tanks "chill" much slower as the % rate of propane being removed starts out pretty low and increases until the tank is almost empty.
If they start to ice around the valve they will stop working. If propane freezes up in a hose or regulator it can cause problems with the gas not being able to flow. It can also condense in a hose and form liquid which blocks the gas from flowing.
using air to warm it doesn't help much since air is pretty still, doesn't conduct heat much, and can get mighty cold as well.
water is your best bet for supplying the heat to keep the liquid propane from freezing.
Water has a pretty good specific heat 1cal/cc and as well when liquid it has convection which can help evenly distribute the heat of the water to the tank. You don't normally think of cold river water as a heat source but compared to an icy bottle of propane its like a nice hot bath.
the water will continue to supply heat to the propane tank even until freezing (at which point 80cal/cc) and you are assured that worst case the ice forming is 32F and the propane is still liquid at that point. Of course you want to change the water out before it starts to ice but if your propane heater has to run all night this should at least guarantee it will still be running in the morning.
If using small tanks, and you have a large supply of them, you can rotate the stock of them and warm them in a bucket of river water.
if its a larger steel tank you might not be able to submerge it in water but you might have to operate it next to/in the river water.