That is a function of how well the tire grips, and it's not surprising that you noticed an increase in stopping distance with only a grand touring tire .. depending of course what tire you were switching from.

From what I've seen, most tires in the sizes that fit the Protege are around 20 lbs ... adding a heavier tire probably has the same effect as adding heavier rims. ( Slightly slower accel and braking )

 

Don't know if this helps at all, but I had a Suzuki Grand Vitara with Falken ZIEX 512 235/60/16 and even in 2WD it did decently in the snow and ice we had this past year and I know it doesn't mean much here, but in 4WD it was great! I know it is a completely different vehicle, but the tread pattern would be the same, so just my opinion.