Yes, u can say that it much beeter in comparison to summer... Cozz the temperature is very good to visit mount abu and the day whether is very pleasant u can roam around city very easily in comparison of summer where humidity and temperature is too much it is not easier to go in that sunlight....
In winter you can travel easily bit one thing is that this is the season of winter and there at mount abu there is cold... The temperature around 3-4 degrees....
If u r comfortable with winter u can easily go there..
Yes, Ofcourse December-January are the best months to explore west parts of rajasthan like jaisalmer, pushkar, jodhpur , bikaner. and later in january end you can visit most of the places and can have great experience.
Visiting Rajasthan during the first month of the year is a real good choice considering the cold will start subsiding and the days will not be unbearably hot. Also a variety of festivals are celebrated every year in January making it easier for you to experience the colours and know about the culture of Rajasthan more in a short span. Here is a short list of festivals for your reference:
1. Jaipur international kite festival ( around mid Jan - Makar Sakranti ) if you are into scenic skies, kite flying tournaments , good food and festive mood
2. Jaipur literature festival : Held in Diggi Palace . A must go for people who loves books and magic and some mind stimulating conversations
3. Bikaner Camel Festival : food, camels, photos and the much more exciting competitions. 4.If you love cars you might like the vintage car Talley which happens in that month in Jaipur and Jodhpur if you are lucky. I hope the above points were informative and useful in you deciding if you want to visit Rajasthan in Jan month or not. P.S. Take some warm clothes as it can get chilly at nights.