Weasel or Stoat at Ynys Hir?

Back in Early Autumn (late September-early October) we visited Ynys Hir. The staff were so friendly and answered all our questions, but there was one sighting I forgot to mention. We spotted a mammal - a weasel or a stoat - coming along the path towards us. It is always tricky to gauge scale on cloudy days, I find, but this creature was definitely smaller than a cat and I think it was bigger than a rat. It was a warm brown with an off-white undercarriage. 

It was on the track coming from the forest to the wetlands, with the ponies browsing either side of us.

Can someone tell me if they know a quick way to tell the difference between a weasel or stoat, besides the old joke?!