Yes, when you go to place the 1Weather widget, you can select a color from the color picker at the bottom of the screen.
The Compact and Tabbed widgets allow you to select background and accent color. The Classic widget lets you select accent color.
Choose your color and tap "OK" on the color picker, then tap "OK" at the bottom of the screen to place the widget.
Currently, on the Classic widget only one color is used for the entire spectrum of the general warmth measurement - full being very warm and empty being quite cool.
If you wish to change the widget color, simply remove the existing widget and make a new color selection when placing the replacement widget.