DOS knows nothing about graphics fonts (mostly: it supports different display fonts which can be loaded using CHCP to change the display's code page, and some other minor details.) It was up to each program to come up with their own method of sending text and images to the printer, generally with the help of a printer driver that contained font metrics for each supported typeface, size and style to help with formatting.
Every program had their own methods for using fonts. Some relied on the fonts in the printer, some had bitmap fonts for each size and DPI combination, and others used scalable fonts (vector, outline, or some other form); many programs used some or all of these methods (Windows still supports all three of these methods too, so DOS programs were not alone with this.) These "soft fonts" were tightly bound to the program, so the format was generally whatever best fit the program: font sharing between programs was not important, nor was it particularly encouraged.
Because there was no standardized format for fonts, there was little need to support standardized locations either. Some programs will have a separate directory for fonts, while others will put the fonts in the same directory as the main program. Programs which supported PostScript or PCL 5 might have an option to specify where additional fonts are located.
TL;DR: Every program was different, and even if you did copy a font from one program to another, it likely wouldn't work because they didn't use the same format (except possibly for PostScript fonts.)