Keep in mind
While I'll be showing pixels of 4x4 images here, that doesn't mean you should work with them. It's always better to work with pixels of 1x1 images and resizing them as they will help you get 0% errors regarding any 1x1 or 3x3 pixels that could be found in the graphic (For resizing, the best program is Paint.NET).
Getting Started
First of all, SMB3 graphics usually have a good amount of color variation, which normally makes it look more realistic, which it's the complete opposite of SMW graphics, which normally have a miniscule amount of color variation. It's important to keep this in mind if you plan on recoloring stuff. Now, say we want to recolor the SMW first castle sign here (made it bigger so it's easier to see al colors and pixels):

As you can see, it's composed only by two defined colors, a orangish-pink and white. This comfirms my previous statement regarding the SMW graphics having a miniscule amount of color variation. If we want to recolor this sign to SMB3 we have to follow the following steps:
- ● Change the colors.
● Add more variation.
● Some extra touches.
Like I stated before, SMB3 graphics look more realistic due to their color variation, but that's not enough to do the trick, we need diferent colors. Let's say we do the following things: We will change the orangish-pink for a orangish-dark brown and we'll change the white for a orangish-light brown.

Add more variation
Now that we have changed the sign colors it is possible to vary its colors, in other words, add a good shading. Shading is the process of giving the graphic a defined position for the sun which will lighten up some parts of it, while darkening some others. This is probably the most important step due to being the most complicated one in most cases, but not this time. Shading comes harder and harder as you learn how to do it, that's why it's better to start with small graphics, like the SMW sign. So let's get started. Let's say we want the sun to be located on the upper-left corner of the graphic, if this is correct we would need to recolor it like the following screen:

Some extra touches
Even if it is already recolored, it still can't be called a recolor if we don't add some extra touches. Let's say we want to add a black outline and change the fill to white for the number like the SMB3 "?" blocks have. To do this we would need to make the number wider, as the size doesn't fit for an outline addition (keep in mind we're working with 2x2 pixels, so do not rush on while doing so.) After we have made it wider, we can proceed to change the number color to white, and make the black outline, which shall look like this:

Congractulations, you have succesfully learned the basics of SMB3 recoloring. Good luck on recoloring some other stuff, hope this was somewhat useful.