We present a near-infrared transmission spectrum of the long period (P=542 days), temperate ($Teq$=294 K) giant planet HIP 41378 f obtained with the Wide-Field Camera 3 (WFC3) instrument aboard the Hubble Space Telescope (HST). With a measured mass of 12 $\pm$ 3 $M\oplus$ and a radius of 9.2 $\pm$ 0.1 $R\oplus$, HIP 41378 f has an extremely low bulk density (0.09 $\pm$ 0.02 g/cm$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$). We measure the transit depth with a median precision of 84 ppm in 30 spectrophotometric channels with uniformly-sized widths of 0.018 microns. Within this level of precision, the spectrum shows no evidence of absorption from gaseous molecular features between 1.1-1.7 microns. Comparing the observed transmission spectrum to a suite of 1D radiative-convective-thermochemical-equilibrium forward models, we rule out clear, low-metallicity atmospheres and find that the data prefer high-metallicity atmospheres or models with an additional opacity source such as high-altitude hazes and/or circumplanetary rings. We explore the ringed scenario for this planet further by jointly fitting the K2 and HST light curves to constrain the properties of putative rings. We also assess the possibility of distinguishing between hazy, ringed, and high-metallicity scenarios at longer wavelengths with JWST. HIP 41378 f provides a rare opportunity to probe the atmospheric composition of a cool giant planet spanning the gap between the Solar System giants, directly imaged planets, and the highly-irradiated hot Jupiters traditionally studied via transit spectroscopy.