There's as many subnormals as there are distinct values with the same exponent, so 2^23 for floats and 2^52 for doubles. This includes the number 0, but you may consider it a special case different from the other subnormals; if so, subtract one. How much of the range they occupy also depends on the interval you're requesting. However, for the common interval from 0 to 1, they occupy about 1/127th of the range for floats and 1/1023rd of the range for doubles.
One can reason to this conclusion by noting that the subnormals have the same effective exponent as the smallest normal number (except that they use the 0.xxx representation instead of 1.xxx; the exponent in question is -126 for floats and -1022 for doubles), and then observing that all normal numbers with exponents from that minimum up to and including -1 are also in the range. Since the number 1 is usually not included in the interval, we can ignore it, but even if it was, it would be the only representative from its exponent (0) anyway, so the effect on the size of the range would be miniscule.
i.e. what percentage of the range do they occupy and how often would one expect to need to sample to obtain one?