It would have an effect. I will be happy to critique your thinking.
Would it mean that the seasons of Winter and Summer would be longer and more extreme? As to how it might have an effect on the deflection of winds, I just can't figure that one out yet specifically. Length of days would not be effected, I think. If rotation speed was changed, the lengths of days would be longer. But if the axis were tilted to approximately 30 degrees, that would not seem to have an impact on the number of hours in our day. Thank you for be willing to help me think through this.
Do you think the seasons will be both longer and more extreme?
I agree that it would not seem to impact the hours in a day (That would relate to the speed of rotation rather than the inclination.), but it would influence the number of daylight hours.
However, since this is not my area of expertise, I searched Google under the key words "earth axis tilt change effect" to get these possible sources:
I hope this helps a little more. Thanks for asking.