What you are referring to is sometimes called 'uprating'. It's the opposite of 'derating', which you'd do to some or all of your components depending on your application and reliability needs.
Here is an old article on the subject of uprating. Their recommendation at the end is a good one -- contact the manufacturer to understand what might be affected by operating at low temperature. They will never guarantee operation outside their limits (unless you are a big/strategic customer for them) but they may be able to provide some guidance on what they would be most concerned about, which could help you formulate a good life test/screen.
The real answer depends on tons of factors. Is it going to see thermal cycles (going between hot and cold) or just operate down at -55C? Thermal cycling induces mechanical failures in bond wires and IC packaging. Is it a 'one off' vs 'mission critical' application, ie., what are the consequences of seeing a failure. If it's a 'one off' (single unit being built for short term use), you might be ok with testing a few units. If it's a mission critical situation, or the part will permanently be operated at a low temperature, you probably will want to spend more effort on the qualification.
Screening like this has been done for military applications for years. The important thing to understand is where the real "cliff" in the parts performance is. We can all agree the parts will probably not perform at -200C. And we can probably all agree the parts will probably perform just fine at -41C (just outside the STM32F operating range). The manufacturer has put in some guard band on their components operating range.
The relevant questions are-- can you figure out where the guard band is (and does it include your desired lower temp range), and will it ever change across multiple lots.
Figuring that out will require testing many parts to get good statistics on the reliability of the parts at low temperature, and what the distribution of their failure looks like, so you can predict if the failure mode is likely to appear in your implementation. And then, once your product is in production, you will have to monitor the parts performance with some kind of acceptance sampling.
An alternate approach to all of this is to install a heater, and use the STM32F's die temp sensor as feedback in the heater control loop. Doesn't help for a cold start but if it's a continuously running unit it might be ok.