Compositions of crosslinked polymers and methods of using such compositions as viscosifiers and fluid-loss control additives in drilling and treatment fluids for subterranean applications are provided. In some embodiments, the methods include: (A) forming a treatment fluid comprising a divalent brine and a crosslinked polymer composition, wherein the crosslinked polymer composition includes: (i) at least one polymer that includes at least a first monomeric unit of one or more N-vinyl lactams; and (ii) a crosslinker selected from the group consisting of: divinyl ether, diallyl ether, vinyl or allyl ethers of polyglycols or polyols, divinylbenzene, 1,3-divinylimidazolidin-2-one, divinyltetrahydropyrimidin-2(1H)-one, dienes, allyl amines, N-vinyl-3(E)-ethylidene pyrrolidone, ethylidene bis(N-vinylpyrrolidone), and any combination of any of the foregoing; and (B) introducing the fluid into a portion of a well bore penetrating at least a portion of a subterranean formation.