This year holi falls on 8th march. In Mathura celebrations start from 2nd March and end by 10th March. In Vrindavan too holi falls on 8th march. Being 9 day celebration it is likely to start on 1st or 2nd of March. Other info will start to update as dates nearby. Will share this tripoto link written by a traveller pertaining to planning travel during Holi to Mathura and Vrindavan see if it is suitable for your travel. https://www.tripoto.com/uttar-pradesh/trips/essential-guide-5c4de726abdbc
To get the most accurate and up-to-date information about the 2023 Holi celebrations in Mathura and Vrindavan, I recommend checking with reliable sources such as official tourism websites, local news outlets, or event organizers in the region https://iogamesio.org/
Mathura is famous for its unique Lathmar Holi, where women playfully hit men with sticks. This usually takes place in the week before the main Holi day. https://mapquestdrivingdirections.app