We've had a lot of people ask this whether they can go without propane in their tiny house. Yes, you can avoid propane and do everything with electricity if you like. Keep in mind that every appliance that heats or cools (coffee pot, toaster, heater, A/C) draws a lot of current. If you're planning to power your house on a PV solar system or by plugging in to an existing house you can dramatically increase the feasibility and affordability of the project by minimizing your electrical needs.
Besides the obvious steps of kicking the coffee pot and using low voltage lighting, here are three suggestions to lighten the load on your electrical system: heat your water with passive solar or compost, collect heat from a passive solar heater, and consider cooking with an alcohol stove.
There are solar hot water options ranging from low tech DIY setups all the way up to sophisticated active and passive solar hot water heaters like these from Rheem or Durda Diesel. Here's a roundup of some videos on DIY solar hot water systems. If you're making large compost heaps you can heat water by running a lot of flexible piping through your pile. Here's a list of quick videos on YouTube about DIY hot water from composting piles of yard debris. If you're really into the DIY angle, you can make your own; check out these wild videos on how to make your own passive solar heat collector with all kinds of components, including soda cans.
You could also consider alcohol as a fuel option for your cooking. Certain stoves run off denatured alcohol which is less flammable (also TOXIC) and isn't stored under pressure - so much safer that it's preferred on boats. Of course alcohol is also a renewable resource which you could conceivably make yourself if you had to. You can get cooktops, or a stove with a built in oven. Alcohol ovens can be quite expensive but I've heard great things about the high end ones from people who are using them. One woman I know of searched for months and found a $2000 alcohol stove with oven that someone was selling barely used - she got it for less than half the price. Here's the brochure for the Origo 6000 Built in Oven with Stove. If you're on a super tight budget and you're able to cook outdoors most of the time you could get by for a while with an alcohol camping stove - they range from DIY versions for a few dollars up to a typical price of $30 - $50. Don't use them indoors!
In short, there is a way to run your tiny house using whatever energy source you prefer, whatever your concerns or budget.
