This will affect local climate in that the ash and dust (as well as the sulfur dioxide) will temporarily decrease the amount of sunlight in the area for a few days. Eruptions like this that spew ash and other material in the air, over a period of time, will have the effect of decreasing the amount of sunlight that enters the earth's atmosphere to hit the surface, which can affect global temperatures, but we are talking about this happening over a period of 25, 50, maybe a 100 or 200 years.
Let's pray for the safety of everyone down there and hope things are alright.