SelecTrac Transfer Case

Does anyone know of a way to test if the selecTrac transfer case in my Jeep is properly engaging in 4x4 hi / part time mode? I have had the fluid changed regularly in it and I am in 2wd mode 99.99% of the time. However, last winter, my Jeep struggled to make it down a flat road covered in slushy / melting snow. My tires were all basically bald with about 60 psi of air so that was probably the problem. But regardless, is there a simple way to ensure that the transfer case is transferring power equally to the front and rear axle? Even with worn tires, I was expecting better performance on a flat road with 4wd...