If you want to do the trek with the path covered in snow then I would recommend you to go in winters. Otherwise you can either go before June or after mid September because between June and September you would find lots of thunderstorm there throughout the day and you wouldn't be able to enjoy its beauty much.
The Trek from McLeodganj to Triund is a sharp one of over 1100 metres and it is absolutely worth it because of the refreshing walks amongst the Rhododendron and Oak Forests. The months of May-June & September-October are the best time to visit this place as it is very pleasant here during these months. and yes it is completely safe.