That's what my question was aiming for. So I take it that Opera Mini seems to include tsl1.2 support. The meego-browser does not, neither does wget or the openssl library in the supplied version.
I'm annoyed about this problem because not only do various sites not load in the webbrowser, but also other apps have problems. E.g. I cannot subscribe some podcasts in gpodder due to this (took me some time to figure out that tls is the problem, since error messages everywhere are very non-specific).

So in principle it should be possible to crosscompile libopenssl in a sufficiently recent version, similar for wget; for the meego-browser I don't know. But I have no idea of how cumbersome this actually would be. Can somebody give me any hints?

Getting the certificate store in order is needed in addition, of course.