That's pretty much what I measured- 160mm.
The winch is round(ish) in its side profile, and what I've found is that my warn XDC-S fits fine, as the grille tapers away with the curve of the winch drum. 
You gain a bucketload of space when you remove the grille (6 screws). Then you can slide the winch up from underneath the bar, then drop the grille back in from above. 
The clearance issue may arise from the clutch engagement lever, but in most models this can be clocked to give it suitable access. 
If you are buying a brand name winch, then you can often dig up the dimensions, and make a cardboard template of the side profile to suit, so you can see it 'IRL'
				
			 
			
		 
			
				
			
			
				-Mitch
'El Burro' 2012 Defender 90.
			
			
		 
	
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