Personally I think hot worked as a sub-classification in glass-making is an oxymoron. Cold worked glass is a very clear term that relates to work done on the piece after it has cooled down. Trying to subset glass with a term like hot worked makes little sense and as seen above does sow confusion. Any process of forming glass has to be hot worked.
Surely there are enough basic process terms available already: Pressed, rolled, cast, spun, blown (with prefixes; machine-, free- (air-), mould- (mold-)), moulded (molded), lampworked (flameworked), and a few others for industrial processes. These can be supplemented with techniques used as a secondary stage, primarily to decorate while still hot. But all are hot worked.