The equilibrium and low-lying isomeric structures of ArnOH (X(2)Pi) clusters for n=1 to 15 are investigated by simulated annealing calculations. Potential energy surfaces are obtained by a pairwise-additive approach, taking into account the open-shell nature of OH X(2)Pi and including spin-orbit coupling. It is found that the spin-orbit coupling suppresses the Jahn-Teller effect, and many of the clusters have high-symmetry structures (C-nnu with n>2) which would be forbidden in the absence of spin-orbit coupling. The structures are generally similar to those previously found for the closed-shell systems ArnHF and ArnHCl, but different from those for the open-shell systems ArnNO and ArnCH. This is because Ar-OH (X(2)Pi), like Ar-HF and Ar-HCl but unlike Ar-NO and Ar-CH, has a near-linear equilibrium structure. ArnOH clusters for n up to 6 have all Ar atoms in a single shell around OH. In the clusters with n=7 to 9, OH is under a pentagonal pyramid formed by six Ar atoms, while the others bind to its exterior, away from OH. For n=10 to 12, the minimum-energy structures have OH inside an Ar-n cage, which is essentially icosahedral for n=12 but has vacancies for n=10 and 11. For n >12, the extra Ar atoms begin to form a second solvation shell. The global minimum of ArnOH may be constructed from the minimum-energy structure of Arn+1 by replacing one Ar atom with OH.