Should Dragon Pokémon be weak to Steel type?
It does sound like an interesting concept, but I'm not precisely sure as to how it would work, unfortunately.
I suppose it's understandable as to how ice-types have strong effect on them (in media, dragons are portrayed to have a tough time under cold climate), as well as dragons and fairy (at least to some regard), but I don't believe I could think of much reason for steel, aside from it being tough to break, hard-hitting, and so forth. If we go by this route, however, a lot of other types could be treated the same, such as rock and ground.
Plus, adding another weakness to dragon would sort of make them... used less, in a way. Currently, it has three, which many of us would agree is a lot, and if there's one more added, I believe we'd be finding ourselves to be more careful when utilizing dragon-type Pokémon and whatnot; those who are new to the scene would likely stay away from them until they develop more experience. Perhaps I'm looking into this too much, I don't know, haha. Though, I still don't feel that having another weakness implemented would be a good idea in long run.