I was hoping that someone more expert would come to the rescue here, Friedrich ! But I shall start the ball rolling.....
I can't answer for 1943/44, but I have found a reference in Bruce Quarrie's book,
'Weapons Of The Waffen-SS ' ( PSL, 1988 ) stating that on 23 March 1940 Hitler authorized the formation of four heavy artillery battalions for the Waffen-SS, which previously had no such equipment. These were totally motorized, with no reliance at all on horses.The book contains a very good photo of a 10.5cm leFH 18 being towed by a SdKfz 11 half-track.
BUT, I am not sure how this situation may have changed later in the war, when motorized transport was in much shorter supply. We know, for instance, of many thousands of horses being killed in the Falaise pocket.
