Depends on the shoes, your surefootedness and your ankles. I did the Horseshoe last month in a pair of Salomon Pro Sticky Lows and they were generally fine, though not as sticky as they might have been. I did semi-turn my ankle walking back to the car park at the end of the day, but that was just sheer carelessness and probably would have happened with boots.
Generally you do lose a bit of stability, mainly because most shoes aren't as laterally stiff, but you gain a bit of nimbleness and dexterity. Personally I'm happier with a pair of lightweight boots though I suspect the impression of ankle support is illusory - stability is really down to the heel cup and lateral stiffness of the sole. Is a soft ankle cuff on a boot really going to present a real physical obstacle to an ankle sprain? I'd still rather have used the Pro Sticky Mids tho.
Also depends on the individual shoe - some are good, some less so. Watch out for sole compounds as well, some of the most common ones seem a bit hard for use in the wet. Eg: Berghaus Vertigo Los.