Is it permissible for someone suffering from urinary incontinence to perform tayammum if repeated ablution and washing or changing clothes due to their contamination with urine becomes difficult, especially in winter with the use of cold water?

If the urine flow stops for a period sufficient for Wudu (ablution) and prayer, then one must wait for it to stop, even if this leads to missing the congregational prayer. Then, one should wash away the impurity, perform Wudu, and pray, without resorting to Tayammum (dry ablution).

However, if one fears that the prayer time will expire before the urine flow stops, then one should purify oneself, bind the affected area, then perform Wudu and pray, even if the impurity flows out. In this case, their ruling is that of a person with incontinence.

It is obligatory to wash clothes or change them if possible without unusual hardship. Otherwise, there is no harm in praying in them.

As for Istinja (cleaning after relieving oneself), wiping with a tissue or similar is sufficient if the urine has not spread beyond its usual exit point. If it has spread, then washing with water is necessary. If cold water is harmful, then it must be heated. If that is not possible and one fears harm, then one should remove what is possible and pray.