Climbing garden plants.
What is the best time to plant garden plants, using a planter pot as the ground is clay?
This really depends which climbing plants you plan to plant. Many of them can be planted as the ground warms up to above freezing. You can either amend the ground to be suitable, or go for containers. Either way will be fine.
This article will help you to amend clay soil: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/how-to-improve-clay-soil.htm