You can go to Dhanolti which is about 30-40 km from Mussorie and you can reach there in 1.5 hours and also visit Lal tibba(which is in the route of Dhanolti) .You can see some snow on the way to Dhanolti. In Dhanolti there are Eco parks(you can enjoy the nature) and adventure spots(like paragliding).
Surkanda devi temple about 8 kms from Dhanaulti is a good news for the trek lovers.You can enjoy a small trek plus temple for prayer which is about 2000 steps.
At the temple you can see snow just behind the "Hanuman Ji ki murti" and enjoy the snow.
Then you can reach to the starting point which is 10-15 minutes down trek. Then you can go back to Mussorie and can see other spots like camel road,gurudwara and you can do shopping(if you are left with time ) .Last bus from Mussorie to dehradun is at 8 p.m. .
You can hire a taxi as an alternative if you miss a bus but extra charges will be applicable after 8 p.m. otherwise the standard taxi rate is Rs. 1250/- only before 8 p.m.
A train named "Nanda devi express" will depart by 11:30 p.m. from the Dehradun Railway Station and you will reach New Delhi by 5:30 a.m. next morning.
I hope this weekend trip experience will help you to plan a trip to Mussorie ( a beautiful place ).
Any queries you can ping me.