Would a native BrE speaker use "may/might/could/can" when talking about both personal experience and general possibility in these examples?
"Earthquakes can/could/may/might be frequent/dangerous. (Generally)
"Earthquakes can/could/might (not "may") be frequent/dangerous here." According to "English Grammar in Context" by Michael Vince "can" is the only option when talking about a general possibility as in sentence 1. I have read that "may" is not used when talking about what is possible based on personal experience as in the second sentence.
"Winters can be cold." Generally. Thus either "can", "could", "may", or "might" is correct here, but
"Winters can be cold here" "can", "might", "could" is correct but "may" is not.