First of all, the winter mode has nothing to do with the 4 wheel system. Winter Mode should work in both 2 and 4 wheel drive. Winter mode simple starts you out in a higher gear rather than 1st. This gives you a different amount of torque to the tires at a lower RPM...the result is that you are less likely to spin the tires when you're starting out. After you get above a certain speed everything will act normal. Occassionally the winter mode on my 97 Rodeo will come on for a few seconds and then turn itself off. I'm not sure what causes this, but try setting it when you're in park and see what happens...maybe this will make a difference. Just keep trying it. If it never works right then you have a problem!
When you shifted into 4 wheel was it 4 High or 4 Low? If you were in 4H moving slow in the snow chances are you wouldn't feel much of a difference at all. If you're not used to 4WD then I suggest you do this (only ONCE and for a SHORT TIME!!) -- go to a dry parking lot and shift into 4H. Step on the gas and drive straight for a second, you should note an increase in the feeling of power. Then try and turn a tight circle -- if the 4WD is working you'll know it! It'll jerk and feel nasty. Do the same for 4L -- and this time it should even feel more powerful and it will really be fun doing a circle! Don't over-do this because driving on dry pavement for an extended period with 4wd engaged is hard on the transfer case! A minute or two will not hurt it.
Also, you should have 4wd shifting instructions on your visor. I have a 97 Rodeo with SOTF (shift on the fly), but I imagine the 91 was the old system like my 94 Trooper. To shift into 4wd in my Trooper I have to come to a complete stop, put the transmission in neutral and then shift into 4wd. To disengage 4wd I have to stop completely, put the transmission in neutral and then back up in reverse for about 10 feet. This disengages the clutches in the older auto-locking hubs.
This should be enough for you to figure out how to properly engage the 4wd and to check that the system is working properly. If this doesn't work, let me know!