I'm planning to install a pair of snow/winter tires on rear axle(because they are about to wear out). The front axle has new regular tires (not winter/snow). Both will be of same spec (205/45R17) I'm wondering and want to know the possible handling/other problems I could experience . my car is front wheel drive.
tl;dr: Don't do it, but if you do, be vigilant about rotating the tires based on the road conditions. Mechanically it will not cause any problems, as there is nothing linking the front and rear axles.
You should always try to run the same tires front and rear. If you only have 2 winter and 2 all season tires, the rear tires should always have more traction. So, if there's snow/ice on the road, put the winter tires on the back. If the roads are clear, or just wet, put the winter tires on the front.
You always want the rear wheels to have more traction because it will decrease your chances of spinning out. If the front tires lose traction before the rear tires, you are in an 'understeer' condition, which is relatively safe as you can still see what you're traveling toward and attempt to avoid any obstacle, straighten the wheels, and stop the car.
If the rear wheels lose traction before the front tires, the back end of the car will begin to swing out. This is called an 'oversteer' condition. Depending on the situation, this is much more dangerous, as you may end up traveling backwards with little control of the vehicle, and no idea what you're heading toward (trying to steer becomes frantic and confusing when you're going backwards).
The chance of encountering an 'oversteer' condition can be exacerbated by trying to slow down in the middle of the corner. Letting off the throttle, or tapping the brakes during a turn will shift weight from the rear axle to the front, causing the front tires to gain traction and the rear tires to decrease traction. Again, if you have higher traction tires on the rear axle, the worst that can happen is your low traction front tires begin to slide. If your high traction tires are on the front axle, the loss of traction for the already low traction rear axle could cause sudden, or 'snap oversteer' (aka lift-off oversteer). This problem is EVEN FURTHER exacerbated in FWD (front-wheel drive) vehicles, where most of the weight from the drivetrain is already over the front axle.