That is a really nice hat, and the fur felt is a very good quality. While it could be seen as a riding hat style, it is more of what would be called a take off on the "Eugenie" or "Empress Eugenie" which is a porkpie style that came into popularity in the late 1860s and has had several revivals over the centuries, once in the late 30s (and the style was worn into the 1940s as you mention). And that style came back again in the later 1980s and into the 1990s, during which time it was extremely popular again. Sometimes the brim is turned slightly up on the 1 side and there would be an ostrich feather.
The Empress wore that style while riding, and you see it in mid Victorian photos and paintings, and so it fits that "riding style "category too. Although technically it is not a riding hat. Sorry to disagree with Melanie, but the "Tally Ho" has nothing to do with the hat itself or the style of it. I have seen that exact same logo on other style hats. That is just the trade name of the fur felt that was imported and used to block the hat by Frank's studio. I knew Frank professionally, and recall the day he died, right before the Millinery Awards in NYC (early 1990s) and I remember the (way too short) memorial tribute they gave to him on stage. But I digress......
I just saw this post and do not remember right off the top of my head when he did his "Private" line of hats, but I think it was around the late 80s to 1990. Although I have a few of his hats with this label that look to be earlier, more late 70s and early 80s.
Whatever the date, it is a nice find. Most hats from that time are (inferior) wool felt. His private line as you might suspect had better materials (yours is a fur felt) overall and was higher priced. Although they still glued on the label!
If I can pinpoint the date better I will get back to you. We have a VFG Trade member here who has access to old news clippings and she might come along and help.
Thanks for sharing the hat, it brought back happy memories.