Horns and pens are most of what I turn and I think that I have the minimum set of tools for that. My tools include:
3/4" roughing gouge
1/8"parting tool
1" skew
1/2" skew
3/8" spindle gouge
3/8" bowl gouge
Robert Sorby 3/4" round nose (graduated profile) scraper
Robert Sorby Hollow Master for bowl turning.
5 piece set of Pinnacle miniature turning gouges (1/16" parting tool, 1/4" skew, 1/4" & 1/8"spindle gouge, 1/4"round nose scraper,)
Most are PInnacle cryogenically treated HSS. When properly sharpened, the edge does hold up longer. I still hone about every 20 minutes of turning.
I use a SuperNova2 chuck with 50mm jaws for the base plugs, and a pen turning mandrel for the pens and horn tips. You will need at least 16" of swing to turn entire horns. I have a Nova 1622-44 and used to use a Jet 1014. Seems to me that most serious turners end up with a PowerMatic which would certainly handle just about anything.
Mark