Since ribbons can be replaced or you can try to place them in hermetic small bags, this looks to be where old dot matrix printers will rule.
I've seen laser printers go for a few years but I wonder if this summer house is subject to temp, humidity extremes.
I've tried several brands/types of printers for my boss's summer house. The printer often goes unused for 6 months or more. The print heads get clogged and fail, whether he removes the ink cartridges or not. My last failure was a HP 576dw (although it appears this model has a high print head failure based on posts I've seen when tried to clear the error message). In fact, removing the cartridges seems to make it fail faster. Laser toner cakes and it seems to mess with the drum. I think a printer that the print head and cartridge are the same would be the best solution, but I haven't found one yet. Suggestions?