from the perspective of a parent with a child of a similar age (well a very almost 3 year old , so close) , children are unpredictable - as un-predictable as animals in some cases. My son who is very farmiliar with our horses, these are 17hh and 18hh drafts, loves on them like they large stuffed animals , and we are lucky that our old boys are very gentle and happy to be adored. Because our horses are quiet and do not mind the enthusiasm of a small boy , he thinks all horses are like this - and so , it is necessary for both our sons safety and the safety of the animal for us to have the rule 'don't touch the animal , you don't know what he may do' - in the same way , we appreciate our friends understanding that , while it may seem like we 'don't trust their judgement' when it comes to their animals (and this is the same rule for any animal ,wether it be a budgie or a horse or anything in between), we are really only looking out for the wellbeing of our son , and not wanting him to do somthing that might startle the animal.
It is not that we don't trust their judgement , it is that we don't trust our son to know if it is ok to pat the horse's (insert part of body here) , or hug their face as he would our two. If you have an animal that is not used to small people , they may not react the same way to the small person as they did to the adult.
I don't know if I am explaining very well at all :S ,
I teach my son to always let the animal sniff his hand first before trying to touch them, but he is small - and enthusiastic. He might think that your horse is such a lovely horse that he just wants to give it a hug , but your horse might be alittle suprised at the small person attaching himself to their leg/face/neck , in what my son would mean to be a happy hug - him showing the animal that they were pretty/lovely animal (he will often say to our big boys 'your a lovely horse " - *hug's face/kisses ear/hugs leg if that is what he can reach* - and they just stand there and take it) but your horse stepping back - note , not being vicious or 'bad' in anyway , just taking a step back to have a better look as horses often do , well if that step back ends up on the 3 year olds foot , well 3 year old feet are alot smaller than adult feet.
Do you kind of under stand what Im saying???
I often worry that I come off as rude or like I don't trust peoples judgement , but it is that I know my son needs to be guided , or better yet picked up (but I cannot do this anymore as he is too big so if his father is not there to pick him up I err on the side of caution just in case) when meeting new animals as he is a small child , and however well behaved he is , and however well you teach him - he can be enthusiastic and is prone to spontaneousness - both of which do not mix well with animals sometimes.
It may be that said child had been having an off day and was being particularly un rulely and she did not know if the child would listen or not? Children can be very trying at times, perhaps she had had a bad morning/ night with the child and her patience was running thin and so she came of more snappish than she ment. Either way , I would not take any offence - unless she said "dont go near the horse , it will bite you/that horse is vicious/badly trained" she probably did not mean any offence. It just came off that way maybe?
And , I use my son just as an example of most small children between the ages of 2 and 5, and myself as the mother if said child.