The ionosphere is a highly rarefied, very high altitude part of the earth's atmosphere, and has essentially NOTHING to do with the weather as we experience it on or near the surface of the earth.  Weather is mostly confined to the lowest level of the atmosphere, the troposphere, with almost no involvement from even the next highest level, the stratosphere, much less the much higher ionosphere.

Even if HAARP were pumping vast amounts of energy into the ionosphere (and really, how much energy can this facility deliver in the first place?), it would not make a bit of difference to the weather on the surface of the earth.