metal any sorts. can be taken in to a local scrap metal place.
i have seen what some folks can do, to destroy land. with nothing but junk and trash. it is like an animal hoarder. for example some old lady with 100 cats in her house. but instead of animals. its everything. even regular house hold garbage. its disgusting.
if this is your case, a tractor with a backhoe with a thumb. can be your friend. though a 4in1 bucket or perhaps a regular bucket and grappel on the front. can help dig stuff up and out of areas.
if the stuff is that old 30 plus years. you should be carefull of old paint. might have lead in it. old treated lumber is bad in burning as well. shingles, tires, other plastics.
============
375 for a dumpster, i would suggest you invest into a trailer. granted you end up paying for gas and then once at dump they end up charging you for a dump fee. but if you have time a trailer can be cheaper than a dumpster. i see dumpsters more of being for contractors and professionals for hire. for a quick fill and removal type of thing.
i honestly think you are over thinking things needing to have something to burn stuff in or on. burn barrel is nice once you have things to a manageable doing. but until then just designate a spot strip the grass and weeds away with a tractor bucket. and start burning on the ground. so what if it does not all burn. after it cools down get a metal rake and pull it back into a pile. and reburn if need be or off to the side. and call it good enough.
as far as well freezing. not going to happen. once you get past the frost line depth for your area. ground temperatures are normally right at 55 degrees F and stay that year round.
on another note. it most likely overwhelming right at this moment. but pick a 2 or 3 spots. one spot for metal stuff and appalinaces (fridges, water heaters, etc..) and other pile for shingles, tires, plastics and like that need togoto dump directly, then another pile errr area for a burn area. ya it is going look like an ugly eye sore for a couple years. but it helps motivate you to finish cleaning the property, and if it comes down to it. makes it easier and quicker to haul stuff to dump. more so if you higher someone to haul it out. having ability to say it will take this many trips can = discount for you. vs having a dumpster hauled away every so often.