A large number of trees are believed to have been felled by strong winds during the storm, and the viewpoint and car park at the managed refuge area near Hawes have been closed to the public.
National Park Authority staff are currently at the site assessing the extent of the damage and debris removal will commence next week, meaning some diversions will have to be put in place for walkers.
The storm's impact is a blow for the 10-year red squirrel monitoring and conservation project at the reserve, only weeks after a report revealed the fragile species had maintained and possibly extended its range in the Yorkshire Dales. There are also small populations of reds on the National Park's Cumbrian borders, but Snaizeholme is their only stronghold in North Yorkshire.
The reserve is a managed refuge area surrounded by a 'buffer zone' in which grey squirrel numbers are controlled. The larger non-native greys push reds out in the competition for food and territory.
In the past two years, the reds have begun to spread out from the reserve into towns and villages including Hawes, Aysgarth, Askrigg, Bainbridge and Hardraw. Many residents have begun feeding them in their gardens, though conservation officers have warned about the potential for dependency on this food source.
The red squirrels' main diet is pine cones, and they only thrive in the long term in areas with significant coniferous forest cover - meaning the destruction of a proportion of their habitat could have a serious effect on the population's continued revival.
Red squirrels became almost extinct in the Dales in the 1960s following an outbreak of squirrel pox and a severe winter, but a small colony was encouraged at the late Hugh Kemp's commercial Christmas tree plantation at Mirk Pot Farm, and later designated as a refuge zone in conjunction with local landowners.