Preliminary note
The question is explicitly about SVG, but the solutions in this answer work with many other formats of pictures and even videos (in principle; videos may be laggy and there will be no sound).
Using characters to represent pixels
Basic general approach: find something that can read the format (SVG in your case) and can use aalib or libcaca.
I found mpv. Example:
mpv --pause --vo=caca 'https://upload.wikimedia.org/wikipedia/commons/0/02/SVG_logo.svg'(Quit by pressing q.)
In case it's not obvious: to view a local file (local with respect to where mpv runs, in your case it will be a file on the remote system) use the pathname of the file instead of https://….
It works, but it does not keep the aspect ratio. Even if it did try to keep the ratio, the character grid in your local console does not necessarily use squares and mpv cannot know how far from squares the grid is.
You can tell mpv how many columns and lines it should use. In my console characters are twice as tall as they are wide, so I need twice as much columns than lines to get a square picture. The following command gives a pretty nice preview for me:
COLUMNS=40 LINES=20 mpv --really-quiet --pause --vo=caca 'https://upload.wikimedia.org/wikipedia/commons/0/02/SVG_logo.svg'(My TERM is tmux-256color. In less capable terminals the result may be less pretty.)
For each particular SVG image you will need to adjust the value of COLUMNS and LINES, so the result looks undistorted in your console.
Note this is not "plain text" you requested. Depending on the value of TERM (which should reflect the capabilities of your terminal) mpv will show you colors and/or blinking characters.
Even better
It turns out mpv can use sixels. If your terminal can interpret them right then use this:
mpv --really-quiet --pause --no-osc --osd-level=0 --vo=sixel 'https://upload.wikimedia.org/wikipedia/commons/0/02/SVG_logo.svg'This is how the result looks in Konsole:
reset may be useful to clear the view later (note: in some cases I needed to run it twice).
Read man 1 mpv; there are several options specific to sixels, you may find them useful.