I doubt if the filly would get thrush by standing outside....thrush is more likely to be found in horses/ponies stabled in dirty conditions.
The main danger in keeping ponies in muddy conditions would be mud fever/cracked heels. This is due to the softened condition of the skin when the legs and pasterns don't get a chance to dry, and the enhanced ability for the causative (soil-borne) bacterium, Dermatophilus congolensis, to enter the skin. It invades the epidermis but doesn't damage the germinating layer, resulting in regeneration, recurring invasion, and desquamation and pus exudation.
The resultant Dermatophilus is recognisable by the presence of lesions and, if left untreated, deep cracks which cause varying degrees of lameness.
Also, be careful if restricting pony's grazing to a small bare paddock, particularly in the spring, as the fructan level in short, stressed (by constant grazing) grass is very high, especially between mid morning and late afternoon. This can be a causative factor in laminitis, and fat ponies are actually safer when allowed controlled access to older, longer, rough grazing, as there is a far lower level of fructan intake this way.