Permissibility of praying in shoes

Yes,
that is permissible, because the Prophet
(peace and blessings of Allaah be upon him) prayed wearing his shoes.
In al-Saheeh it is narrated
that Abu Sa’eed said: The Messenger of Allaah
(peace and blessings of Allaah be upon him) lead us in prayer whilst
he was wearing his shoes, then he took them off [whilst still praying],
and the people took their shoes off too. When the Messenger of Allaah
(peace and blessings of Allaah
be upon him) said the Tasleem
[at the end of the prayer], they said: “O Messenger of Allaah, you took
off your shoes, so we took off our shoes too.” He said: “Jibreel came
to me and told me that there was some dirt on them, so I took them off.
When any one of you comes to the mosque, let him look at his shoes,
and if he sees any dirt on them, let him wipe them. And they can be
purified with dust.”

(Narrated
by Abu Dawood, no. 650).
The point here is that praying in shoes is permissible. It says in the
hadeeth: “Be different from the Jews, pray wearing your slippers or
shoes.” (Narrated by Abu Dawood, no. 652).
But the condition is that the shoes must be taahir (pure, clean). If
there is any najaasah (impurity) or dirt on the shoes, then one should
not pray wearing them or enter the mosque in shoes, unless he is sure
that they are free of impurity or dirt. And Allaah knows best.