It seems that, to receive the name of white light, it may or may not contain contributions of the non visible range of the spectrum. So white light may be considered a class containing several different states of the EM field.
There are many definitions of "white light", none are truly quantitative. For example:
"Apparently colourless light, for example ordinary daylight. It contains all the wavelengths of the visible spectrum at equal intensity."
"light perceived by the eye as having the same color as sunlight at noon."
"the complete mixture of all of the wavelengths of the visible spectrum."
Some are contradictory, e.g. sunlight at noon does not have equal intensities of all wavelengths in the visible spectrum. But none that I found excluded radiation of nonvisible wavelengths. Herschel discovered IR by noting that there was energy in "white sunlight" beyond visible red.