As long as it's warmer than -45°F, you're fine.
A single event of holding pee won't harm you. It takes several days of constant prolonged holding till you develop the condition (forgot the name) when your bladder will start sending signals it's full (even if it's not). This is reversible (even if problematic), from personal experience.
A much more imminent issue is exactly how freezing is it and what is the wind-chill? It's going to be basically impossible to find yourself at the place where peeing would be painful just due to air temperature. From experience, peeing at -40°F air (zero wind-chill) is not painful at all, merely cold. So, it probably takes another 10-15 degrees to reach that point and those places are very isolated and hard to get to.
Wind-chill can be however quite painful. Way, way, way more painful than inserting camera into your bladder at the doctor's office. I don't know if it's a cold tolerance, but I peed dozens of times at around -40°F wind-chill (it's basically omni-present for up to 8 weeks per winter here in North Dakota) and it was fine.
However, once at around -50°F, the sensations and pain was quite horrendous. I could feel a quite sharp and strong pain way deep inside my body and cold spreading to other neighbouring tissue around the bladder. My bladder was still quite sensitive next morning and it was still a bit painful.
You just might prefer to choose to avoid that experience.