If I had a UK passport which was due to expire on February 1st, 2020 - less than 6 months from now, would I be allowed to make a weekend visit to Germany?
As I understand it.
Under the brexit deals that were negotiated by the government but not passed by Parliament there is supposed to be a transition period lasting at least until the end of 2020. Freedom of movement would continue during this transition period. So you would be ok to travel in February on your existing passport.
On the other hand, in the event of a no-deal brexit it is most likely that the Schengen area would treat UK visitors like other foreigners which means you would need a passport that was issued within the last 10 years and with at least 3 months validity beyond the end of your trip, so your passport would not be acceptable.
This is a badly formed question because your passport expiry is the same as the Brexit crash-out date! So you are only asking about 2 use cases: a) Britain still in EU, or b) passport is expired. Black-boxing Traveler's link: After a crash-out Brexit, you cannot travel on an expired passport end of inquiry.
Anti-DV Disclaimer: I'm referring to a UK citizen traveling to Germany, since that is OP. I answer questions in context.
FYI, after a crash-out Brexit, your passport becomes useless for German travel 9.5 years after its issuance, or within 6 (not 3) months of its expiry, whichever happens sooner.
If you're asking "well, what happens on a yes-deal Brexit?", ask on politics.se because that depends on the deal. Nobody knows. The link assumes the only thing we do know, which is crash-out.