There's nothing wrong with plastic mountaineering boots. I help teach and guide a beginner mountaineering course in the PNW - we tell people just starting out to get whatever they can afford, as long as its crampon compatible, and I see a lot of used plastic boots come through. Probably because they're indestructible and, yea, a lot of people use them once for some guided climb or course, so there's a healthy secondary market. I think I've seen the same pair of boots come through the course on different students at least once.
They tend to be warmer and more waterproof, but they're heavier and some would say less comfortable. Some "old timers" swear by them. But they are definitely "old school". I think the only company which still makes a full plastic climbing boots is Koflatch (and I think Scarpa still makes the Inverno, but threatens to discontinue it every year). They tend to be a bit overkill, unless you're climbing Denali or in the Himalaya or something. They used to get used a lot as "rentals" by guiding companies (again, comparatively cheap, durable, will probably keep your client's feet from freezing off)
Don't worry too much about the "plastic going bad" or whatever. Most reputable brands are made out of Pebax or similar cold-malleable plastic.
But, if you have the money, I would recommend a light weight "super-gaiter" style boot for cold weather climbing. I have the Aku Aurai DFS (picrel) and love them - they're almost as light as my regular boots and they're comfortable enough for long approaches. I even use them when snowshoeing, and sometimes for just shoveling snow off the driveway.
