2001 santafe awd pulling to side occasionally

Winter has arrived and i notice recently the steering wheel feels like it is being pulled to the side usually left. I never noticed this until road conditions have become slippery,and snowy.
This was never a problem before. only thing different I have 1 newer tire on the back and 3 older tires on the rest of the vehicle,the tread pattern is the same build up of snow and ice under vehicle affecting a sensor maybe? combo of 3 older tires and 1 new affecting awd? thanks for all responses
zenox
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Even without AWD, it is never recommended to replace one tie on an axel.
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Took it for a drive tonight and noticed hesitation in the steering when making a turn. i mean , turn steering wheel and front wheels are slower to react to steering wheel motions. power steering fluid level is good. z
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