Yup. The Dragoon regiments' Horse Grenadier companies even had bearskins to boot. The Cuirassier regiments' Carabinier companies had no obvious distinction, other than the fact they carried carbines, while most other cuirassiers of the time only had pistols (iirc 12 men per 'regular' company had carbines). Sometime after the SYW they combined all the Horse Grenadiers and Carabiniers together into a couple of permanent regiments.
As it happens, the old 30-per-pack Old Glory Austrian Dragoon packs were over-populated with Horse Grenadiers, with about six of them per pack. I bought a load of packs to make Saxon Chevauxlegers and Reichsarmee Dragoons, but they didn't have Horse Grenadiers, so had a shit-ton of bearskinned cavalry figures left over. However, Wurttemberg had a complete Horse Grenadier regiment (red coats with black facings - very nice), so they will come in handy after all.