Is it permissible for a person to intentionally seek hardship in worship, desiring reward, such as performing ablution with cold water when warm water is available, or going to a farther mosque when a closer one exists, based on Al-Shatibi's statement that whoever deliberately seeks hardship will not be rewarded for it?

The mukallaf (accountable person) is not rewarded for hardship if he intends it for its own sake. Rather, he is rewarded for it if it accompanies an action he is commanded to perform, because Islamic law does not intend hardship for its own sake. Thus, whoever intends hardship merely to increase his reward, like one who performs Hajj on foot to make it difficult for himself, has violated the intention of the Lawgiver. The hadith "Your reward is commensurate with your toil" does not refer to toil intended by the mukallaf, but rather to the toil that occurs in worship and was not intended by the mukallaf. Using hot or cold water for ghusl (ritual bath) is permissible and expansive, because the religion of Allah is ease, as Allah Almighty says: (Allah intends for you ease and does not intend for you hardship).