We present preliminary trigonometric parallaxes of 184 late-T and Y dwarfs using observations from Spitzer (143), the U.S. Naval Observatory (18), the New Technology Telescope (14), and the United Kingdom Infrared Telescope (9). To complete the 20pc census of >=T6 dwarfs, we combine these measurements with previously published trigonometric parallaxes for an additional 44 objects and spectrophotometric distance estimates for another 7. For these 235 objects, we estimate temperatures, sift into five 150K wide T_eff_ bins covering the range 300-1050K, determine the completeness limit for each, and compute space densities. To anchor the high-mass end of the brown dwarf mass spectrum, we compile a list of early- to mid-L dwarfs within 20pc. We run simulations using various functional forms of the mass function passed through two different sets of evolutionary code to compute predicted distributions in T_eff_. The best fit of these predictions to our L, T, and Y observations is a simple power-law model with {alpha}~0.6 (where dN/dM{propto}M^-{alpha}^), meaning that the slope of the field substellar mass function is in rough agreement with that found for brown dwarfs in nearby star-forming regions and young clusters. Furthermore, we find that published versions of the log-normal form do not predict the steady rise seen in the space densities from 1050 to 350K. We also find that the low-mass cutoff to formation, if one exists, is lower than ~5M_Jup_, which corroborates findings in young, nearby moving groups and implies that extremely low-mass objects have been forming over the lifetime of the Milky Way.