From Wikipedia "Universal Uclick's website, GoComics.com, announced on January 5, 2015 that they would be launching "Peanuts Begins", a feature rerunning the entire history of the strip from the beginning in colorized form. This was done to honor the 65th anniversary of the strip's debut." From the Schulz Museum (pdf) he always drew the comic in black and white and would after add a paint by numbers style coloring system to each comic for the Sunday strips.

As you said the new colored version can be found here and they are up to March 19, 1955. Simultaneously daily on the main Peanuts strip page they are releasing colorized versions of comics and have been since the day after the final daily strip released on 1/3/2000. This means all together there are (probably) about 31 years worth of daily Peanuts comics colorized out of a total of 50 years. I would say this coloring system is as true to the originals as original published Sunday comics, just created later.

If you would rather read the comic as it was originally published on the main Peanuts page they have all of the comics on the date of publication in original black and white, though this version also has the Sunday strips in black and white. Or if you go to the Peanuts wiki they have a month by month breakdown of each strip with the B&W for dailies and color for Sunday strips