Assessing Wardrobe's Protection from Sunlight
No, your clothes won't fade from sunlight.  They may take heat damage, but only if the cloth is very high end, e.g., silks, etc. and if the area has no A/C.

As for the wardrobe itself, it will take some damage, but if you keep the drapes closed (and if those directly next to it are reasonably opaque), then it will take years for fading to occur.