Our production service has always supported UDFs, though the free sandbox service does not.
Unfortunately, Postgres makes it difficult to install extension modules without superuser. That said, we've wanted to support contrib modules for ages. Lately, encouraged by the work Dimitri Fontaine has been doing on extensions, we have a pilot project going which includes support for hstore, pgcrypto, pg_trgm, and of course, postgis. Feel free to contact me at pvh(at)heroku.com if you're interested in taking it for a spin.
I looked for any more documentation about that, but the only official word I have from them in the past is the support ticket I filed last year stating that they don't support "additions" like user defined functions or the various contrib modules.