Gorilla tracking activities are conducted throughout the year in both Rwanda and Uganda by their respected National Parks Authority. This includes Christmas day and all public holidays. The season does not stop the tracking activities although certainly to be the forest in torrential rain will make the trekking tougher. At the same times you could consider this to be a free bonus to your package as what is being in the heart of a rain forest all about!
June, July and August are the months when you should least expect rain in the forest. The dry season happens to be the months when permits are in highest demand primarily because of the European and North American summer holiday window when the majority of visitors to the parks choose to come to Uganda and Rwanda.
The actual tracking experience can be gruelling at times and for some a long day, whilst for others they are back in camp some 3 hours later having located their group closeby.
The viewing experience on the Virunga in Rwanda is very different in respect of the density and type of vegetation to that in Bwindi Forest. Both viewing experiences are usually exceptional and if you do not have a bench mark of having trekked before who is to say what is a good trek or what is a poor trek by comparison. For most this is a once in a lifetime experience and simply awesome. Maybe you should look at some UTube videos to see other peoples experiences as there are many there to view.
Where you trek will in the end probably be dictated by where you can get a permit. Permits are in high demand throughout the year although between Feb and April you will have more options.