Samsung Galaxy 10, go to date and time, you can now choose to select timezone by UTC offset, not region. If you select -3.00 on the phone, the Gear S3 will also show the correct time.
I just want to share my recent experience,
So I've got my S3 Frontier in June 2018 which I pair with a S8+ since, then I travel often between USA and Brazil, so changing time zones as well and never had any problems so far but this December I noticed an 1 hour forward on the watch comparing to the phone. I started to gather info ending up on this post. So shortening a long history it's far simple to set manually the date and time on your watch, all you got to do is unpair the watch of your phone so you will be able to set the time and date but to keep those settings you will have to keep your smartwatch on stand alone mode which from my opinion that's useless, basically you are exchanging all the features of the pairing mode by a "current" date and time set.
I think, in my case, the real problem is the time zone in my country now, basically here in Brazil, Sao Paulo, it was expected a daylight savings system which was canceled previously by the government, so this region of Brazil was supposed to be set on GMT -2 but it's actually GMT -3, then on paired mode for some reason you can see the phone sets the time based on the network which is GMT -3 Brasilia Standart Time, then when you check the watch it shows GMT -2 Brasilia Summer Time. It seems to me there's a mismatch issue between the times, I would say the watch has something to do in order to reflect the phone set. What I did and it's working fine is set the time zone manually on the phone using Buenos Aires time zone as reference which is also GMT -3 with no daylight saving observed all year long, then the watch keeps the same time as on your phone. If I find any other issues related to that I will post later.