From the manual it says the abs/esp system works best when on winter tyres. . . .
This is basically because of the diameters. The closer the diameters are, front to back, side to side, the better the ABS/ESP system works. (At least in the sense of knowing what is going on. If the ABS/ESP could be reset/calibrated for the set of tires/wheels on the car, it would make little or no difference.)
You can easily calculate the "ideal" tire diameter from the information on the tire sidewall. (This of course assumes the tire is inflated properly, on the correct rim, etc.)
So, 205/55R16's = 205mm section (tire) width, with a 55% tire height . . . (As compared to the section width.)
Ideal tire diameter = 16" + (205 x .55 x 2)/25.4 or 24.88 inches
That would be for my fronts, and the staggered rears would be 225/50R16's . . .
ITD = 16" + (225 x .50 x 2)/25.4 or 24.86 inches. (a negligible fraction smaller.)
The only way to get 0 difference is to have the same tire size on the same rim width at all four corners. (Inflated to the same pressures, same wear, etc.)
I would believe that the Manual is considering that the absolute performance on winter tires is of less importance than stability and control. From my research, it's almost impossible to get a staggered set of wheels to match 100%, but considering what the differences are with the OEM tires, something within a percent will typically give minimal problems. The "sport" option on the 170 is just over 1%.
The only time the ABS/ESP kicks in is when it thinks a tire is sliding beyond a certain amount; so the larger the tire delta, the closer to the edge the system already thinks it is. What you don't want is a delta so big that the ABS/ESP sees the different tire rotational speeds and thinks that a tire is sliding all the time, or every time you turn a corner. (In which case you would have to turn it off.)
Although mixing and matching brands isn't considered the best thing to do, keeping the same type/age/wear of tire on the same axle is desirable!! There is also some new thought to keeping the better/newer tires on the rear axle (assuming you have that choice) since most cars are already setup to lock up the fronts before the backs. This is to keep the car from swapping ends under panic braking, (very undesirable) and new tires on the front/old tires on the back tends to defeat that objective. (This is true for dry, wet or snow.)
Some things to think about anyway.