Oh, that does sound miserable. But sounds like you need to do someting about that stove! It sounds as though its a major part of your problems.
A heat pump is one option but be warned, they work least well when its cold (yes, I know! but its thermodynamics, folks!) and I wonder how many have been tested down to -20? Very important to get really good advice. When it is that cold and your house has stone walls it might not be able to keep you warm, ideally a heat pump needs large radiators as it puts out low temperature heat - think a big warm radiator rather than a small hot one, for the same heat). Air source pumps are about £7-9k I think, and you get a repayment every year I believe, its the renewable heat incentive. Ground source work better but you need to dig up the garden and that totals about £20k. And they still need electric to drive the pump - quite a bit though about 1/2 to 1/3 amount compared to direct electric heating (they will claim more saving than that, but may not have been tested in Scotland).
Actually with the RHI you might be able to get an income back to help "bankroll" a much better efficient wood stove (though not coal) - if you are wedded to wood. I think it is dirty and more trouble than its worth myself, unless you have room to grow your own or 'know a man who does', but I know lots of people love it.
I know oil delivery and even secure storage can sometimes be tricky in remote areas, but a proper condensing oil boiler might be a better bet, look into that? Ask neighbours what the cost is and how reliable local delivery firms are? (there is also calor gas, stored in a giant gas cylinder (you know those grey things, bit like an oil tank) probably costs more? but I find oil boilers smelly, I know, I am very fussy!!)
For a similarish cost eg maybe £10-£15k I think?? you could get your stone walls insulated. External works far the best, we had it on our 2' thick stone walls and I can honestly say it has transformed our house, great with the damp/mould too, as walls are now warm inside. Ours cost £20k but it is a very big 4-bed house + annexe. You do need enough overhang from eaves as is about 6" thick (unless you also need a new roof at the smae time, we waited till the roof needed doing too). Can be done internally as well but have to be a lot more careful, you lose a bit of space, and you lose the benefit of all that warm stone. Plus the bl**dy builders come in the house) Would still make a massive difference however.
There are grants and loans for this too, I think you have warm front still in Scotland but that may be income dependent? There was supposed to be a government scheme called ECO too but that has been mesed around so there may not be anything there, done via energy companies and also some construction firms. Google ECO (energy company obligation) and your county maybe? And sometimes better offers for people currently dependent on solid fuel as you are, google that too!
Scotland better at this than England, also some local authorities run their own schemes too
Also look into what the repayment on a mortgage extension is assuming you are owners - compare the repayments to say saving half your wood bills, on a yearly basis? You might find you are breaking even and in return you will get a warmer more comfortable house, especailly if you do insulation.
RE all the draughtproofing advice etc - the stove is going to be sucking in air to burn (we have an inlet direct to stove that does not whistle past our feet!) but do take care a) that enough air is getting to the stove so it can draw properly (unlikely to be a problem, but still, carbon monoxide danger if not drawing properly). You should get a carbon monoxide monitor anyway with solid fuel. OR gas. Actually everyone should have one!!)
... and b) that you are getting enough ventilation as you don't want mould growing, can be a probelm on cold stone walls in coolish rooms.
well anyway essay over and I do hope you sort something. I will tell my kids to stop moaning that we haven't had any snow: they wouldn't last 5 minutes in your house by the sounds of it.