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The rule for the Helical Targeting Array reads, "If the contempor remains stationary in the movement phase, it gains the skyfire and interceptor special rules for that game turn."

Question: If a contemptor dreadnaught is immobilized, may it only snapfire at ground targets for the rest of the game?

Nope. In a turn it does not move for any reason, including being immobilized, it will have sky-fire and will have to snapfire at ground targets. If the immobilized status is somehow removed (techmarine for example) the dreadnought will be able to move the following turn, and if it does it will loose skyfire and be able to use its full BS at ground targets again.

When do I need to declare that my Dreadnought is using its helical targeting array, and does it remain active for the rest of the game from then onwards?
The use of these is entirely optional and should be declared by the controlling player at the beginning of each of their game turns, with the caveat that the Dreadnought must remain stationary. When the helical targeting array is not used on any given turn, the Dreadnought may fire its weapons normally at ground targets.

from The Horus Heresy 7th Edition Warhammer 40,000 FAQ and Errata December 2014

ah, even better.