For an existing Tiny House that has decent insulation a ductless mini-split may be all you need. It's an air-air heat ex changer that runs ~97% efficient and is reasonable priced, easy to install(no ducts). Check Mitsubishi and Fuji they can help size the unit. If you tie them to PV they can get you off the grid.
If you have access to electricity, a simple space heater will likely be fine for your winters. We've found that a single baseboard heater increase the temperature in our 200sqft tiny house by about 60*. On the days it dipped below freezing, we simply had to cook something and our place got nice and toasty.
I'm not sure about cooling options, since it doesn't often get above 85* here.
For On-Grid cooling we usually install a small window unit into the wall of the house. They usually cost less than $100 and a really easy to install and use. We have also installed mini-split systems for people but those run about $2000 installed. Then if you have a service call it's $150, which is more that an entire window unit. But some people like them because they look a little nicer (but you pay for it!)
posted 4 years ago
Air flushing by way of windows will not work in many climate zones throughout the world with humid freezing and/or humid hot , toxic, outdoor environments that by doing so can make matters much worse. Some stay above 70 Relative Humidity (RH) levels all year which is the floor level for microbial generation on building materials that needs to dry out in 48 hours. The ideal RH for humans and building’s is 30-40% that should be maintained at all times, AC is one way, a hydronic radiation space heater is another especially if there is interior mass to couple it with. If not there may be more health related and building repair expenses in time that far exceeds active devices. We cover this extensively with input from PHD’s in my thread here: https://permies.com/t/48019/natural-building/Indoor-Air-Quality-Healthy-Building