Can I legally run wiring through a window or its frame?
First, does the window open, and is it required by fire codes for emergency egress? 

If so, you could remove the window and install a shorter or narrower window, that still meets code, and then use the margin to pass through your utilities.  I would use fairly tough metal conduit for electrical to make it resistant to damage. 

I already see a wood margin that might suffice.  

Otherwise you'd want to permanently remove the window from service as a window, by doing a surface treatment on both sides that renders it not a window.   Either remove the window entirely or panel it over on both sides so it is entirely buried, remove a pane, put the service through, and fill the voids with insulation.  

I hate to remove a classic window like that made of solid material and well installed, so I would go for the remove-a-pane option.