Pulsar wind nebulae (PWNe) have been established as the most populous class of TeV γ-ray emitters. Since launch, the Fermi Large Area Telescope (LAT) has identified five high-energy (100 MeV < E < 100 GeV) γ-ray sources as PWNe and detected a large number of PWN candidates, all powered by young and energetic pulsars. The wealth of multi-wavelength data available and the new results provided by Fermi-LAT give us an opportunity to find new PWNe and to explore the radiative processes taking place in known ones. The TeV γ-ray unidentified (UNID) sources are the best candidates for finding new PWNe. Using 45 months of Fermi-LAT data for energies above 10 GeV, an analysis was performed near the position of 58 TeV PWNe and UNIDs within 5° of the Galactic plane to establish new constraints on PWN properties and find new clues on the nature of UNIDs. Of the 58 sources, 30 were detected, and this work provides their γ-ray fluxes for energies above 10 GeV. The spectral energy distributions and upper limits, in the multi-wavelength context, also provide new information on the source nature and can help distinguish between emission scenarios, i.e., between classification as a pulsar candidate or as a PWN candidate. Six new GeV PWN candidates are described in detail and compared with existing models. A population study of GeV PWN candidates as a function of the pulsar/PWN system characteristics is presented. © 2013. The American Astronomical Society. All rights reserved.