I worked for several years in the converted tackroom of an old horse ranch, with a (heavy) extension cord to the nearest power, which was 50' away. So it can definitely be done.
However---a plug strip is not a good idea, in general and particularly if you will be running a space heater which will be one for hours at a time. In fact, the NEC requires a dedicated outlet for loads like ovens, space heaters, and air conditioners which will be on for more than some number of hours at a time.
Since I was going to eventually bury a power line, I went ahead and wired the building with its own subpanel, and made the cord-to-building connection outside where overheating couldn't do any damage. (The other end of the cord was in a dedicated, GFI-protected outlet.)
An oil-filled convection heater held the temperature just fine, although where I am the outside air rarely drops below about 30 F. Since I use a Metrolux enlarging timer, the (noticeable) voltage drop when the space heater cut in was not a problem; without it, printing would have been a nightmare.
The same power setup didn't work out quite as well in the summer; I put in the smallest air conditioner that I could find, and it struggled any time the temperature went above about 85 F (this is in a 6x12 room with 5-1/2 inches of insulation in the walls and ceiling!). When I eventually put in the permanent wiring (#10 wire in buried conduit) I discovered that the air conditioner compressor had been tripping off due to undervoltage, leaving the fan running to disguise the problem. (It works fine now).
If you are going the power-cord route, I would strongly suggest using the largest cord you can manage. A 12-gauge cord is marginal beyond about 100 feet, but the cost of 10-gauge will probably exceed that of UF cable or wire buried in conduit. You should feed from a dedicated circuit with ground fault protection unless you are going to put in a subpanel in the building (in which case you will either need or already have more expertise than I have to share!). Finally, don't underestimate the starting-current requirement of an air conditioning compressor. I did, and to this day I'm still a bit surprised that the thing even survived.
(I could share a lot of accumulated experience with water supply, etc. but I suspect that you will hear more of that than you have any use for
)