In some contexts. It seems a little odd to bring it up if someone suggests going to Starbucks. In that situation, it does seem over the top. "Coffee run?" "No thanks. I plan to retire at age 40 and spend my time biking around the city and learning to oil paint. In order to do that, I need to save 50% of my current income, so I've cut out all wasteful spending." Weird.
But if the subject of retirement or where we see ourselves in 20 years comes up, then I'll likely mention it. "Husband and I have really cut back on things and we hope that by the time he gets out of the military, our savings and his pension will be enough that we are able to retire. He'll probably keep working, and I may as well, but it will be because we choose to. It's meant sacrificing some things, but I want to be able to not work far more than I want another pair of shoes most of the time."
You gotta judge your audience and your situation. Otherwise, it can come off as preachy and boastful. And yes, if you have family that might see you as a source of "assistance" if they know your financial situation, keep your mouth shut. As far as my brother in law is concerned, "we have no extra cash", which is true since none of our money is superfluous. It's all got a purpose, but that purpose is retirement, rather than a payment on a Ford Excessive and financed sofa set.