Is it permissible to perform ablution (wudu') while having plasters on the nose that prevent water from reaching the skin, knowing that they are applied at night and remain until after dawn?

It is permissible to use a medicinal patch that prevents sleep or causes harm, and it is not obligatory to remove or replace it if doing so entails hardship or high cost. One may wipe over it and wash the rest of the face. However, if it is possible to replace it without hardship or financial cost, then it must be removed during ablution and replaced.