Pixel size when changing from geographic to projected coordinate system?

I have a large raster dataset spanning ~5 degrees of latitude N-S. I know the geographic projection has a spatial resolution of 0.00025 degrees, meaning that the dimensions of each pixel in meters varies depending on latitude.

I have counted the number of pixels in the raster representing different land cover classes. How would I go about converting these pixel counts to area in m2 if the pixel dimensions are variable?

Would simply converting to a projected coordinate system (ie in ArcGIS) standardize the pixel dimensions so that I can multiply pixel counts by a constant area?