Aha, I have found the reason an icon wasn't set. I have selected "Task Shortcut" among Taskter's widgets instead of "Task" one. With "Task" widget action to set widget icon does work.
The thing is, I need label-less widget, and "Task Shortcut" gives me it. But icon settings doesn't work at this case. I have tried to find the way for action to change task's (rather widget's) icon, but wasn't lucky yet.