Sikkim is fine but Tawang will be challenging. It will be full of white snow and riding will be difficult. Make sure to carry lot of packed food and warm cloths. Also plan a break journey to Bondila-Green Valley- Near Shila top and then to Towang.
As suggested by Sikkim Tourism, the best time to visit Sikkim is either between March and May or October and mid-December. If you want to witness the blooming natural beauty in Gangtok best season to visit would be in spring, from March to May. Autumn, on the other hand, brings the clear view of Himalayan Range.