I wouldn't say they will come up noe matter how long you wait to refinish them...
Oak hardwood floors generally show wear after about 10 years - that means scratches in their surface, and some high traffic wear. Because they are grey... that is a bit confusing to me. That might mean that the varnish is entirely gone, which wouldn't be a good thing. The reason is that you can actually wear the floors down in the high traffic areas and your floors would be uneven, or take an incredible amount of sanding to refinish at that point.
I have heard that refinishing the floors is a crazy mess, evn when they say they are catching all the dust, it goes everywhere.
The important thing with hardwoods is to get all the dirt off them as frequently as possible. It's the dirt that is wearing them down - small grains of sand trapped under a shoe or foot grinding into the wood. So clean them with a dust mop often. When you clean them with water, we used a hardwood floor cleaner machine that sucks up all the water which makes it really easy - we do that once a week with about a tablespoon of their cleaning solution. It lasts a long time though. Some people use vinegar and water to clean, that is probably fine too.
I would have a professional come assess your floors. Don't commit, but at least hear what they have to say. You don't want to have to replace the floor.