The short answer
Your doorbell chime went quiet once it got cold. in most cases, that's either a weak transformer that finally ran out of push or an exterior button that's corroded or frozen.
The good news: this is one of the more DIY-friendly electrical problems in a house. The low-voltage side (16 to 24 volts) won't hurt you.
The catch: the transformer's other side is live 120V, and that connection is where you need to be careful or call a pro.
Start simple. Press the button and listen. Then test the transformer with a multimeter. That two-minute check tells you which half of the system to blame.
Why winter is when doorbells die
Doorbell systems are simple: a transformer steps 120V down to 16 or 24 volts, that low voltage runs out to a button by the door, and pressing the button completes the circuit to fire the chime.
The weak link in winter is almost always the button. It sits outside, unprotected, and every freeze-thaw cycle pulls moisture behind the faceplate. That moisture corrodes the tiny contacts.
Corroded contacts do one of two things. They oxidize until they won't make contact (dead chime), or they bridge into a short (also a dead chime, but now your transformer runs hot all day).
The transformer is the second suspect. Most homes still run the original 16V, 10VA unit, and after 20 or 30 years, output sags. A transformer putting out 11 volts might ring fine in July and fail once winter adds resistance everywhere.
Then there's the wiring itself. Bell wire is thin, 18 to 20 gauge, and it oxidizes at screw terminals. Metal contracts in cold, so a connection that barely held all summer can open up on the first hard freeze.
Last, don't rule out the breaker. If the transformer shares a 120V circuit with something you only run in winter (a space heater is the classic), an overload can trip the breaker and kill the doorbell along with it.