Without knowing what strength of ND filter you were using, or under what lighting conditions, I can't give a specific answer. However, a little bit of back-of-the-envelope math can help give you an idea of the magnitude of the problem.
Assuming you were shooting a brightly-lit scene under bright midday sun, without any ND filters, the Sunny 16 rule states that at ƒ/16, a correctly-exposed shot requires a shutter time that is the reciprocal of your ISO. With an ISO of 200, the shutter speed should be 1/200.
Again, assuming you were shooting under Sunny 16 conditions, your shutter speed was overexposed by log2(2 / (1/200) = 8.6 stops. Because you were using ƒ/22, we can reduce that overexposure by one stop, down to 7.6 stops of overexposure.
Subtract from 7.6 the strength of your ND filter (I'm guessing 1 or 2 stops, probably). That is how much your long exposure shot was overexposed (again, for typical Sunny 16 exposure conditions).
If you were shooting a snow-covered landscape on a bright sunny day, you'd actually be overexposed even further, because of the light reflected from the large area of landscape. On the other hand, if there was some partial clouds, slight haze, or you subject was partially shaded, then your scene might not have been quite so overexposed by the amount calculated.
However, this gives you a rough idea of what to expect when trying to shoot long exposure shots in midday sun. You tend to need a lot of ND filter to keep the shutter open for 2 seconds. In your case, a minimum of a 6-stop ND filter: ND1.8 in Lee/Tiffen nomenclature; ND64 in Hoya/B+W/Cokin nomenclature. See also: How to read ND filter description?