New Horizons should have some instrumentation to answer that about the mag field. I would suspect Pluto does have a mag field while the atmosphere is in the gaseous phase.
New Horizons is not flying a magnetometer. The two particle instruments are SWAP (Solar Wind Around Pluto) and PEPSSI (Pluto Energetic Particle Spectrometer Science Investigation). However, the particle instruments would detect a magnetoshock or magnetotail, as they are currently doing at Jupiter.