Don’t expect winter weather down at McLeod/Dharamsala, Shimla etc in mid-March . Well above zero in the shade already , double digits in the next week or so.
Explore mentioned cities
The OP and travel companions appear to be from the Philippines. Winter may be relative.

Jaipur, the capital of Rajasthan is also known as the Pink City. It has its own importance when it comes to the celebrations of festivals and fairs. Do you know that the state of Rajasthan due its vivid cultural richness and different festivals, also often called Rangeelo Rajasthan, which means colorful Rajasthan. The houses during the festival decorated with different rangolis, ladies managing households prepare traditional cuisine such as Gunjiya, Papdi, sweet Shakarpara and etc. Whole market is decorated with vibrant colors of Holi. You can literally see the zeal of the festival in the locals while watching them purchasing the Gulaal (dry color), water colors, Pichkaris and sweets for Holi celebrations.

Mathura that the love life of Krishna and Radha sprouted and grew. The entire city is full of Holi excitement. However, for ‘the original Mathura Holi 2019’ you must land up in Barsana and then visit Nandgaon, Braj, & Vrindavan. Spend a day in Barsana and get a feel of the platonic flirtations of Radha Krishna. Folks from Nandgaon come with colors to Barsana and paint the women here. The women too reciprocate and try to defend themselves by playfully beating these folks. Visit Nandgaon the next day as women from Nandgaon visit Barsana with colors. Vrindavan Holi and Braj host Holi in the temple premises where the priests shower blessed holy water(of course colored) on the revelers. Holi in Vrindavan turns the entire city into a riot of colours that is a must see.
I am not sure what you will do in Delhi for many days, I guess 1 day is enough for Delhi and you must travel other nearby attractions like Jaipur, Udaipur which will tell you about the true history of India. And I just read this article the best time to visit Udaipur and I guess your duration is the best to visit Udaipur and Jaipur

Hey guys, thank you so much. Yes, @Lifesupport we are from the Philippines and we really want to experience cold weather. I have been to India last 2016, thanks also to your suggestion back here.
okay, so from all of your suggestions I just revised my itinerary:
12 Manila to Malaysia
Malaysia to N.Delhi (we bought our tickets just now)
13 spend one day in N.Delhi
take the bus going to Manali
14-18 Manali - skate boarding in Solang?
18 night manali to chandigarh
19 morning take the train going to mathura
19 - 21 Mathura for Holi Festival
21 bus to Agra
21-25 Agra for Taj Mahal *
26 morning train/bus to jaipur
26-30 jaipur
30 early bus/train to delhi
31 fly out going back to manila
Note:
* Im planning to go to Taj Mahal on Monday 25th of March just to avoid too much crowd on weekends, but i think 4 days and 3 nights in Agra is too much? plus, we will be wasting weekends or few days just to wait for Monday. thoughts?
Do i need to book my bus and train tickets in advance? especially for Manali, since it will be peak season and also for Mathura

Still raining and above zero at night now in Manali , snowing and subzero day&night at Rohtang top. I would expect to go well above 3000 for stable snow -maybe.
- Im planning to go to Taj Mahal on Monday 25th of March just to avoid too much crowd on weekends, but i think 4 days and 3 nights in Agra is too much? plus, we will be wasting weekends or few days just to wait for Monday. thoughts?
I wonder if you are over-estimating the weekend crowd; especially as you plan to go early in the day. That is a long time in Agra although there is plenty to see and do both in and around Agra.
https://www.lonelyplanet.com/india/agra/attractions/agra-fort/a/poi-sig/449177/356509
https://www.lonelyplanet.com/india/agra/attractions/itimad-ud-daulah/a/poi-sig/449183/356509
https://www.lonelyplanet.com/india/agra/attractions/akbars-mausoleum/a/poi-sig/449179/356509
https://www.lonelyplanet.com/india/agra/attractions/jehangirs-palace/a/poi-sig/1324905/356509
https://www.lonelyplanet.com/india/uttar-pradesh/fatehpur-sikri
However, that aside, and whilst I wouldn't recommend back tracking, you might want to go to Jaipur before Agra.
https://erail.in/trains-between-stations/mathura-jn-MTJ/jaipur-JP
And then go to Agra, and then to Delhi.
If you still think you have days in hand either spend them in Delhi, or there are other options around Rajasthan.
Or from Mathura go a little further to Gwalior for a couple of days
https://www.lonelyplanet.com/india/madhya-pradesh-and-chhattisgarh/gwalior
https://erail.in/trains-between-stations/mathura-jn-MTJ/gwalior-jn-GWL
then Agra and Jaipur in whichever order you prefer.
Do i need to book my bus and train tickets in advance? especially for Manali, since it will be peak season and also for Mathura
Bus tickets usually a day or two before travel and in country is fine.
Train tickets are another matter entirely. The short answer is "yes" and book today. There are myriad options around this but the easiest thing is to book in advance. Certainly ask questions here. I am guessing you do not have an IRCTC account, so once you have fixed which trains you need, Google for a "train ticket please".

Manali...raining... Massive amounts of snow at the Rohtang La ( 3987 meters ) ..Snowfall at the top , prime avalanche season in the middle.
SASE , the snow & avalanche centre in Manali , issued an avalanche warning yesterday. More snow & slush to come during the weekend , all the way down to Manali .

However, that aside, and whilst I wouldn't recommend back tracking, you might want to go to Jaipur before Agra.
https://erail.in/trains-between-stations/mathura-jn-MTJ/jaipur-JP
And then go to Agra, and then to Delhi.
If you still think you have days in hand either spend them in Delhi, or there are other options around Rajasthan.
Thanks! My friends thought of that too. or maybe we can just celebrate Holi Festival in Rajasthan instead in Mathura? then go to Agra and then Delhi? and do you know any good hostels or hotels in Mathura? there are tons in google result tho, but maybe you have something to recommend :D
Thanks guys again I really appreciate all the help.













