When I lived in Russia, a friend of mine spoke Russian sign language and I asked how they managed to communicate in the cold winter months outdoors. They told me using a lot of facial expressions, body language, and that you can sign a surprising amount even wearing gloves.
Mittens apparently are the equivalent of gagging somebody though.
It’s been tried. There’s International Sign Language (ISL) and it’s about as successful as Esperanto. I’ve mostly heard it’s used a little at large Deaf meet ups and conferences.
American Sign Language (ASL) is often the second sign language non-Americans learn as it has a some international presence.
But ultimately sign language users are no more likely to decide on and widely adopt a universal language than spoken language users.
It's sad to see that British Sign Language and American Sign Language are different even though they both came out of societies with a (mostly) common language. I'm sure there are good reasons why it turned out this way but sad that people who already have a communication obstacle ended up with an additional one when it comes to these two large and highly connected societies.
Until 200 years ago most places didn't think Deaf people were capable of learning. With no schools there was less Deaf culture and fewer codified signed languages. It's an awful history.
ASL is more similar to French sign language. Thanks to Thomas Gallaudet, who founded a school in 1817 in Connecticut. Gallaudet was American but studied in Europe and learned about teaching Deaf people in part from a French school.