Resolving the phase structure of neutral hydrogen (HI) is crucial for understanding the life cycle of the interstellar medium (ISM). However, accurate measurements of HI temperature and density are limited by the availability of background continuum sources for measuring HI absorption. Here we test the use of deep learning for extracting HI properties over large areas without optical depth information. We train a 1D convolutional neural network using synthetic observations of 3D numerical simulations of the ISM to predict the fraction (f_CNM_) of cold neutral medium (CNM) and the correction to the optically thin HI column density for optical depth (R_H_I__) from 21cm emission alone. We restrict our analysis to high Galactic latitudes (|b|>30{deg}), where the complexity of spectral line profiles is minimized. We verify that the network accurately predicts f_CNM_ and R_H_I__ by comparing the results with direct constraints from 21cm absorption. By applying the network to the GALFA-HI survey, we generate large-area maps of f_CNM_ and R_H_I__. Although the overall contribution to the total HI column of CNM-rich structures is small (~5%), we find that these structures are ubiquitous. Our results are consistent with the picture that small-scale structures observed in 21cm emission aligned with the magnetic field are dominated by CNM. Finally, we demonstrate that the observed correlation between HI column density and dust reddening (E(B-V)) declines with increasing R_H_I__, indicating that future efforts to quantify foreground Galactic E(B-V) using HI, even at high latitudes, should increase fidelity by accounting for HI phase structure.