I wouldn't attempt to move it right now. Such mature rhododendron should have an extensive root system which you inevitably will damage during the transplantation and it will have a hard time to settle during the winter which eventually will be coming. By doing that in an early spring you'll give it more favorable conditions to adjast.

About full sun. My notion is that here, in New England, you could easy get away with rhododendrons, kalmias and andromedas planted in a full sun for as long as you provide ample moisture during the first few years after planting and mulch them well. In your particular case, I think, established rhodie not necessary should be moved, it will adjast itself to the larger amount of sun it getting in a couple of years if you will help by providing regular watering during those transitional years.
BTW, North-West exposure is where my rhodies/kalmias are most healthy, vigorous and floriferous and practically have no winter damage no matter how harsh winter could be.

I agree that your success would be limited unless you had the ability to move a very large root system. The time of year is no problem since it is dormant. The problem is that the stress created by seriously damaging the root system would be complicated by winter desiccation.

Also, sun stress on a plant on the NW side of a house is minimal. What it really has is wind stress in the winter. If it looks stressed I would give it winter wind protection (either antidesiccant spray or a burlap screen). Also, I would test the soil. Rhododendrons need acid soil. I would also think of fertilizing if there is a lack of vigor. Be cautious, rhododendron don't like too much fertilizer, just enough to restore vigor. They also need well drained soil. If this area is heavy clay or moist, then the plant would be struggling.

If you are serious about moving this plant. I would root prune now. That means going around the plant with a spade and cutting down to contain the roots in a space you can include in a root ball when you move it. This will cause the roots to form a more dense mass that can be more easily transplanted. Then next fall or the following spring, the plant would be ready to move. You can transplant a rhododendron any time if you can preserve the integrity of the root ball and water it after moving until the shock of moving has gone. It is just easier to do when the plant is dormant.

Here is a link that might be useful: Rhododendron Culture

The rough 'rule of thumb' is you can relocate a rhododendron any time of year when it is not in active growth ( the period immediately following bloom ) including while blooming, or the ground is not frozen. However, best results follow when you observe the same timing as recommended for planting new shrubs in your specific gardening area. I wouldn't stretch the 'ground is not frozen' to include a temporary thaw.

I couldn't address the sun vs. winter wind siting issue -- rhododendrons adapt to any and every exposure here in this mild climate - exception very dense shade.

Yes, rhodyman is right, if you still planning to move it, root prune it in a spring and relocate in a fall or the following spring. 35 y.o. rhodie should have a very a extensive root system and you don't want to lose a large portion of it.

I'm always so impressed by the extent of knowledge demostrated by Gerdenweb members!

From your responses, it sounds as though the plant may just be stressed from the sudden change in amount of sun. Also, the soil around here is very clay-y - I live on one of the richest (?) veins of clay in the region, which was great for the brickmaking industry, but challenging for gardeners.

The temps don't show any signs of dropping, and the ground has never really frozen solid yet this winter. But, gauranteed, if I decide to start digging - it will!

I will purchase some of that anti-dessicant spray, and add some nice mulch. (I have a huge compost heap). I'll watch it closely and see how it does in the Spring with some TLC, fertilizer, and more water. Thank you so much.

Actually it is not the sun per-se, but desiccation. When a plant is not dormant, and even to some extent when it is "dormant" the plant uses moisture. It gets this moisture from the roots. When you move the plant, you are loosing many roots and hence reducing its ability to get enough water. Then if it is exposed to sun, wind, heat or any other stress that creates a demand for water, it is stressed, extremely stressed. Root pruning months before moving is the best way to avoid excessive root loss. The next best way is the anti-dessicant spray. The third is to shade the plant from the sun and wind until it has time to reestablish its root system. Also, try to keep it cool or avoid moving just before it starts getting hot and new growth is demanding large amounts of water.

Here is a link that might be useful: Rhododendron Culture