The title suggests
The oddly-numbered squares are colored, and the few numbers we have support that theory. Also supporting the theory is the fact that about half of the squares are colored.
This means the colored squares are 1's or 3's, the white squares are 0's or 2's.
The few numbers we have force a few of the first lines, and from there I just followed the slitherlink clockwise around the grid filling in numbers as I went.
Some rules I used:
If the line bordered a white square, it had to be a 2.
If three lines couldn't fit around a colored square, it had to be a 1.
This is my first ever attempt at a slitherlink so hope I didn't miss anything! It was fun!
The starting point:
The point between the two 3's must have a line going to it from each of the "3" boxes, so these two edges are forced no matter what:
Since the box to the left of the "0" is white, it must be even. It's bottom edge must be a line, as the line connecting to the lower "3" can't head in the direction of the "0". This means that this white box must be a "2", and further, that one of the two edges shown in red here must exist:
Looking at the white box above the top "3", it must be even and cannot be a "0". Therefore it is a "2", and the only valid edge remaining is the top edge, which must be a line. From this point on, following that top line to the left and right around the grid is straightforward, as the edges of the puzzle constrain it significantly (versus trying to solve starting from the interior of the puzzle).