I switch things out. I really enjoy the process. It's a bit of a ritual, helping me mark the change of seasons and prepare for what's ahead mentally and emotionally as well as practically. I use it as a time to plan capsules, edit, and make my shopping list.
I do two big changeovers (fall and spring) with a couple of smaller shifts in between when I move out (for example) my heavier sweaters and make way for a few lighter weight ones (in cool spring), or add some jackets while subtracting others.
Keep in mind that I live in a climate of extremes. I find it jarring to look at heavy woollens and light silk and linen sleeveless tops at the same time. If I lived in Vancouver or Seattle and more of my wardrobe was truly cross-seasonal, I probably wouldn't do this.
I'm fortunate in that I have a hall closet right outside the bedroom that is very large. In it, I have a small chest of drawers there and hanging space. I just rotate my things from closet to closet. But if the weather takes an unexpected nose dive, it's all there for me to get it, just a few steps away from my regular closet.
In the past, when I wasn't so blessed, I always found other ways to do this. For years, when I lived in apartments, my out of season clothes went into a blanket box that also served as a coffee table.