In order to explore the physical conditions in winds from pre-main-sequence objects of low, or intermediate, luminosity, we present observations of Pa-beta, Br-gamma, and Br-alpha lines in a sample of 15 T Tauri stars. The line luminosity ratios compared with model calculations, and, while they conform in general to theoretical predictions for cool and neutral winds, they appear of questionable utility for determining the physical conditions within the wind. A better understanding is achieved when hydrogen line luminosities are combined with Na I absorption spectra. This method is here applied to 13 stars to derive (or set limits on) the wind kinetic temperature T(g) and the mass-loss rate M. The resulting values fall in a rather restricted range, for both T(g) (5000-7000 K) and M (10(-8) to 10(-7 M. yr-1). While this narrow range can partly result from selection effects, it is nevertheless indicative of neutral mass-loss periods as a common phase of pre-main-sequence evolution of low-mass stars. We also note that (1) the luminosity of the observed H-lines is consistent with the expected emission from pure winds, with no particular need for contributions from other components (disks, boundary layers, chromospheres etc.), and (2) isothermal winds appear as a viable approximation, at least for the formation regions of the lines under study (i.e., for the inner 1-2 stellar radii). For the seven objects which have been searched for associated molecular outflows (three detection and four nondetections), the wind M values are in agreement with those inferred from outflow parameters. This confirms the scenario in which outflows are driven by fast stellar winds via a momentum-conserving shock propagating into the surrounding cloud. We propose, on the basis of a high M, three good, not yet observed, candidates for CO outflows around T Tauri stars.