In winter you can basically camp anywhere you want (as long as the area is safe and you would not destroy environment). Practicing snowshoes and crampons depends on the snow amount and its quality; therefore, it may or may not be a good exercise. Due to the same factors (and also depending on the car you would take) you may or may not get as far as Whitney Portal.
Practicing snowshoes is the best in fresh, soft, powdered and deep snow which you may hopefully get in the incoming winter. Practicing crampons requires the opposite conditions--firmed to icy snow and preferably steeper slopes. Of course, you can use them in not very suitable environment, but then again the exercise would not provide much benefits.
However, the most important factor in winter adventures is weather. Make sure you not only know the current forecast but also the exact meaning to you and your experience.
There are many pictures and links on this forum that you can explore the conditions of this route and plan your trip accordingly. Come back just a few weeks before your trip and ask the same question to incorporate current snow conditions. For now check out a few pictures of this route I took over my previous winter trips to get the idea what to expect and where to camp.
01/13-15/200601/24-28/200401/10-13/200402/13-17/2003A frozen creek at Whitney Portal

I am planning to do Whitney this winter as well (in January). I will be shooting video which I will post at YouTube for a public access. So far I've posted several videos from Mt Shasta.
http://www.worldofadventures.com/marcus/videos.htm Climbers in the videos are usually inexperienced or with limited mountaineering experience. Hopefully prospective mountaineers would learn something about the specific route and various conditions as well as the mountaineering environment in general before undertaking the challenge.
If you feel like you would like to climb MT or MR with us (from BA) this winter, send me an email. The time spent in the mountains may be 3 to 5 days, depending on the conditions. Summit is not guaranteed, however. To be clear, I am not a commercial guide, I am just a passionate mountaineer.