What formula would I used to change a range of cells a different color
based on the current date?

For example if I have a date of 1/1/2015 in a cell can I change
adjoining cells a different color based on the current date?

Sounds like a job for Excel's "Conditional Formatting."

For example, suppose 1/1/2015 in cell A1, and you want to highlight cells B1:H1 when A1 is after the current date.

Then select B1:H1, use the "Conditional Formatting" command with the formula
=$A1TODAY()
and choose the format fill color of your choice.

The exact way to choose the "Conditional Formatting" command and its options depends on what version of Excel you have. If in doubt, try Excel's built-in "Help."