President Reagan yesterday nominated G. Ray Arnett, who served as head of California's Department of Fish and Game for seven years, as assistant interior secretary for fish, wildlife and parks.

The nomination was cause for some rejoicing at the headquarters of the National Wildlife Federation here. Arnett has been a director of the organization for 17 years and served two terms as its president. He also is a founder and chairman of the Wildlife Legislative Fund of America and its companion organization, the Wildlife Conservation Fund of America.

But the smiles have a slightly brittle edge -- enough advance budget-cutting information has trickled out for environmentalists to know that the scalpel has been raised over some of their favorite programs, and Arnett's ability to prevent major incisions is a question mark.

"He'll have a tough row to hoe," a spokesman for the federation said yesterday. Just how tough won't become evident until the Reagan budget -- by all accounts an elegantly carved piece of scrimshaw -- is unveiled today.

"Money is what talks," the spokesman said. Noting that Arnett was working at the Interior Department in an acting capacity while the cuttable programs were being identified, he added that if conservation programs come out emasculated, "We'll know he doesn't carry much weight."