Hi everyone,
I'm planning to drive from texas to california from December 25 to January 6 2017 but this is my first time driving this route and really don't know how the weather conditions be? And my wife and my 2 years old son also come with us

You're driving from the largest of the lower 48 to the second largest and expect there to be one route?

Where in Texas are you starting?

Where in Cali are you going?

And considering you're within 10 days of the trip, you can go to weather.com and learn the weather conditions of wherever you're driving.

BigRuss has very good points, but especially checking weather.com.

Also, in California, Caltrans has a website specifically for road conditions and weather related information.

http://www.dot.ca.gov/cgi-bin/roads.cgi

We always use both websites when traveling in California, especially in winter. For example, the coast Highway 1 is sometimes closed because of rock slides or wash outs. Or the Grapevine on Highway 5 is closed for ice or snow. When that happens, we change over to Highway 101, which is a scenic route but takes a bit longer that the 5 or much less time than the 1.

Either fly or take the train amtrak.com and rent a car when you get to whichever city in California you want to go to.

It's a really long boring drive if you take the I-10, been there, done that but in July not winter.
Good point though, where in Texas are you leaving from and where in California are you driving to? California is bigger than Italy.

We have no idea if trains make any sense (likely not though) since we have no idea where the OP is starting/traveling to. We also have no idea if flying and renting a car makes sense since we don't know if the OP must use their own car for some reason (like maybe they are moving out here) )

So until the OP returns and fills in the blanks no one can give helpful advice/suggestions.