Uh - no, that part shouldn't make any difference. (pony's barefoot too)
No horse likes deep mud. She's just rather bull headed about it. They all have to be pushed to some degree into slogging through muddy spots on trail. The trouble with her was, she'd take ecurbh through the brush to go around it. :~D Just needs work.
The other aspect that doesn't really occur to them probably is that she's at an advantage in the deep suck mud. It'll pull the shoes right off a shod horse.
Yikes!