What you are considering is what 'old time' farmers did - kept a small flock through the winter, hatched out (or let hatch) as many chicks as possible come spring, let them grow until fall when all but a few went to 'freezer' camp for the winter use - those few were the foundation for the next year's flock. However, with the creation of fast growing birds, a new 'breed' if you will emerged - the broiler.
Generally speaking, heritage breeds were the ones farmers kept 100+ yrs ago - most get to 'market' weight by 17-20wks old. But by then, their meat may not be suitable for today's palatte as it's firmer, tougher and not what we're used to any longer.
Decide on what you are seeking - trying to keep a few broilers alive through the winter is all fine and good. But remember, these creatures are designed to eat! They do eat more feed than other breeds, which will increase your costs to keep them. Depending on where you are in Texas, you might get away with foraging them to offset feed costs throughout the winter. Here in Illinois, that doesn't work for me! However, I'm a firm believer in experimentation! Try keeping them through the winter one year - keep track of all costs and see if it's a viable option for you.
As for our decision, we have Black Java's (a heritage breed) for eggs. We've purchased Freedom Rangers for meat. I can tell you the Freedom Rangers have eaten WAY more than the Black Java's ever do. But they've doubled their weight thus far every week, where the Java's doubled weight in 2 weeks or more depending on individual. The growth rate of Freedom Rangers is phenomenal! And that's the difference between a 'layer' and a 'broiler'. Black Java's were the market chicken of choice at the turn of the last century...but growth is nothing compared to today's varieties.
I hope this helps - if a breed like this existed, the hatcheries would go out of business. For none of us would ever buy new chicks again, we'd hatch out our own!