I can suggest an interesting book which elaborates on different ways on how to influence the climate and with possible consequences. "Hack the Planet" by Eli Kinitsch. Of course if you will make it rain somewhere, this moisture may not come down on another region which needs it as well.
I will try to answer your question from the cloud physics point of view, i.e. mine. Cloud seeding and climate are in general two areas separated by a large difference in time and space scales. Moreover, seeding clouds for making rain happen is still a very debatable topic in cloud physics and the efficiency of rain production is subject to a hot scientific discussion.
However, in principle the thing is doable, but the scale is very small, i.e. that of a single cloud or a cloud field of limited extension. Thus, thinking of influences on climate per se is a rather long jump and does not make much sense to me. If you mean by "climate" a sort of regional effect on precipitation amount, then things obviously change and they must be statistically evaluated against a non-seeded situation.
Finally, the fact that moisture has to come from somewhere is also a subject of discussion and needs careful evaluation with regional models. Anyway, please keep in mind the clear separation between seeding, which is cloud physics/meteorology, and large scale effects that belong to the climate concept. In the middle you fit everything. In other words, trying to influence the climate just with seeding exercises is out of question because you would need resources, and also possibly knowledge, we don't have at the moment, not at all, at least from what I know. Effects are thus quite local at the moment.
I agree with preopinents. Furthermore, even if - ideally - we could have the resources needed, applying them on a part of the geosystem doesn't mean that we could control the effects. The geosystem is largely shaped by nonlinear processes that limit the predictability. In this context, the effects could be highly unpredictable.