Is It Legal For A Landlord To Shut Off Water To A Unit Due To The Tenant Leaving The Water Running To Avoid The Pipes Freezing?

Location: New York State, Tompkins County

In the housing development where I live, the landlord company sends out monthly newsletters. As the temperatures are getting dangerously cold, they have included in a recent newsletter that if we leave the water running to avoid frozen pipes, they will shut off the water until the issue is satisfactorily rectified. On it's face, this seems to violate the warranty of habitability. It's like shutting my water off because I used too much. The only justification I can see is that it might look like a leak, which would be an emergency, which they can then shut off the water to fix, but wouldn't the newsletter constitute admitting that they know it's not a leak? Additionally, preventing the pipes freezing potentially prevents damage to the property like burst pipes. For more background info, our pipes have frozen multiple times this year already and last year as well. Last year, they also sent this notice out in the newsletter around this time. So is this legal? Does a newsletter like this constitute advance notice and a specified timeframe?

ETA: The pipes *are freezing* overnight, very frequently. In fact they are frozen right now. But for some reason they don't seem to burst. I live in a very old unit with paper-thin walls. It's incredibly drafty. Even keeping the thermostat at 75 or so in winter (we pay for heat, they pay for water) still leaves some areas of the house feeling like 50s inside. Basically all of my pipes are exterior pipes and the point where the pipes freeze is just as soon as it comes into the house, so when the pipes freeze, but don't burst, there is no cold water anywhere in the unit. Somehow we tend to still have the hot water. Maybe it's just what was already in the tank. Its temperature varies but it often comes out scalding and almost always has to be mixed with cold for any skin exposure, even in subfreezing temps, and I don't know how long it will last. This means the toilet/bidet doesn't fill/work, I can't wash dishes or shower safely (best bet is to fill the tub with hot water and hope that melts the ice, or, on days like today when it doesn't, wait a few hours for the tub water to cool so I can bathe in it, which means my fiance can't shower or bathe before work) and I have to not use the toilet or carry bowls of hot water to the toilet tank to flush. I also work from home, and the cold temps will likely last all weekend due to the snowstorm. I am also interested in hearing if there is a difference in the answer depending on whether the hot water goes too or not because on this current freeze, the hot water is not as hot as usual, so I'm concerned that even that could go if it gets much worse. I understand that still having hot water might not constitute as much of a problem as having no running water at all, but I could just be getting lucky with that and I'd rather not have freezes at all.