They were one squadron, but they operated totally independently of the rest of the regiment, which remained in India, while the Mounted Squadron was deployed to the Arakan, so the dress of the mechanised squadrons can't really be taken as an indicator of the dress of the deployed mounted squadron.
Ethnicity is a very complicated subject in the Indian Army – many regional regiments (e.g. Punjab, Baluch, etc) were made up from a number of different ethnicities, which would be segregated by company, squadron, platoon or troop. So for example, a Punjabi battalion might have two companies of Sikhs, a company of Hindus and a company of Muslims.
In terms of ethnic dress, Sikhs would never give up their turbans under any circumstances, as it was a religious requirement. The Jats however, wore bush-hat or battle-bowler in Burma.
Just to add to the problems, the Gwalior regiments belonged to the 'Indian States Forces' – i.e. they belonged to a quasi-independent statelet and not formally to the Indian Army proper. I believe that the 3rd Gwalior Lancers were dominantly Muslim, so no religious dress requirements there.
However, Indian cavalry regiments were/are VERY conservative and did go into action in Persia and Iraq wearing full field service rig with turban and lance.
I agree that they would most likely be dressed and equipped as mounted infantry (probably with the cavalry-issue leather bandoliers rather than webbing)
but I'd love to be proved wrong, as it would make a very interesting wargames unit (and figures with turban and lance are relatively easy to find!).