You'd want something like a NEMA 4 outdoor cabinet. They can be expensive, so finding a used one is a good idea unless you have a large budget. Depends on how much room you need, though. If it's a small repeater with built in duplexer and no external batteries, then a small cabinet is easy to do. If you start adding a bunch of batteries, then you'll need substantially more room and will need to address hydrogen venting.
Think: traffic light signal cabinet. We've used them at work.
Cell carriers use some fancy ones that can be set up with add on cooling/heating.
Railroad signal cabinet.
I have some repeaters that are in very remote locations that are fairly well access controlled and repeaters are in fiberglass or heavy plastic cabinets. They work just fine if vandalism isn't an issue at your location.
Keeping them warm/cool hasn't been an issue. We have a small thermostat controlled 12 volt fan to get some airflow through the cabinet. Heat buildup hasn't been an issue, but then again these are land mobile repeaters, not amateur repeaters with wind-bag users.
Cabinets are either silver or white, which helps with heat. The repeaters themselves have generated enough of their own heat to not be an issue in the winter. Usually drops down below freezing at these sites, but not much more than high 20's.
Not ideal, but I've seen some wireless internet providers use contractor style tool chests/job-box style cabinets. You can pick up different size versions of those at Home Depot.
Only issue I've had with this is dealing with bug ingress. Always seems like they find a way in.
And one good habit to get into is smacking the cabinet with a stick or something before entering it. Always polite to let any critters that have taken up residence in the box to know the land lord is there and give them a chance to escape.
