I've had two significant bird strikes at night, each at 10,000', both about 0100 in the morning. One in a Cessna 182, and the other in a Learjet 35A. The Cessna was messy, but undamaged (it was a big bird), and the Learjet's radome was shattered and the copilot side windshield damaged.
Birds are found in instrument conditions. I've found them there. I have no idea how they maintain their attitude or their direction, but I've seen birds, usually larger ones, in IMC on occasion.