  Ultracool dwarfs represent a significant proportion of stars in the Milky
Way,and deep samples of these sources have the potential to constrain the
formation history and evolution of low-mass objects in the Galaxy. Until
recently, spectral samples have been limited to the local volume (d<100 pc).
Here, we analyze a sample of 164 spectroscopically-characterized ultracool
dwarfs identified by Aganze et al. (2022) in the Hubble Space Telescope WFC3
Infrared Spectroscopic Parallel (WISP) Survey and 3D-HST. We model the observed
luminosity function using population simulations to place constraints on
scaleheights, vertical velocity dispersions and population ages as a function
of spectral type. Our star counts are consistent with a power-law mass function
and constant star formation history for ultracool dwarfs, with vertical
scaleheights 249$_{-61}^{+48}$ pc for late M dwarfs, 153$_{-30}^{+56}$ pc for L
dwarfs, and 175$_{-56}^{+149}$ pc for T dwarfs. Using spatial and velocity
dispersion relations, these scaleheights correspond to disk population ages of
3.6$_{-1.0}^{+0.8}$ for late M dwarfs, 2.1$_{-0.5}^{+0.9}$ Gyr for L dwarfs,
and 2.4$_{-0.8}^{+2.4}$ Gyr for T dwarfs, which are consistent with prior
simulations that predict that L-type dwarfs are on average a younger and less
dispersed population. There is an additional 1-2 Gyr systematic uncertainty on
these ages due to variances in age-velocity relations. We use our population
simulations to predict the UCD yield in the JWST PASSAGES survey, a similar and
deeper survey to WISPS and 3D-HST, and find that it will produce a
comparably-sized UCD sample, albeit dominated by thick disk and halo sources.
