Praying while wearing shoes

Performing the prayer while wearing shoes is permissible if they are pure (not stained by an impurity).

The basis of this ruling is the Hadeeth narrated by Sa'eed Ibn Zayd may Allaah be pleased with him who said: "I asked Anas may Allaah be pleased with him: "Did the Prophet sallallaahu `alayhi wa sallam ( may Allaah exalt his mention ) use to offer prayers with his shoes on?" He said: "Yes.”

There is also the Hadeeth narrated by Shaddad Ibn Aws may Allaah be pleased with him that the Prophet sallallaahu `alayhi wa sallam ( may Allaah exalt his mention ) said: "Act differently from the Jews who do not pray in their leather socks or their shoes."
[Abu Daawood]
There is no difference in this ruling on whether the prayers are performed in a mosque, a house, or outside, or in the desert, for the general meaning of the Hadeeth.

Some Ahadeeth even prove that performing prayers in mosques with shoes on is permitted as reported by Imaam Ahmad and Abu Daawood may Allaah have mercy upon them and narrated by Abu Sa'eed Al-Khudri who said: "The Prophet sallallaahu `alayhi wa sallam ( may Allaah exalt his mention ) said: "If one of you comes to the mosque, he should look and if he sees some dirt in his shoes, he should wipe it out and pray in them.”

Moreover, Abu Hurayrah may Allaah be pleased with him narrated that the Prophet sallallaahu `alayhi wa sallam ( may Allaah exalt his mention ) said: "If one of you performs the prayer and takes off his shoes, he should not cause harm (discomfort) with them to anyone (beside him). Rather, he should keep them between his feet or offer the prayer while wearing them." [Abu Daawood]

Besides, Abu Sa'eed Al-Khudri may Allaah be pleased with him narrated: "While the Prophet, Sallallaahu  'alayhi wa sallam, was leading the Companions may Allaah be pleased with them in prayer, he took off his shoes and the people behind him did likewise. When he, Sallallaahu  'alayhi wa sallam, finished the prayer, he asked them: “Why did you take off your shoes?” They replied: “We saw you taking off yours.” He said: “Gabriel may Allaah exalt his mention came to me and informed me that there was some impurity on them.”

source -->  Mu'uminīna Şādiqīna