Yes, linen can be worn any time of year. The style of clothing often dictates the appropriateness rather than the fabric.
PROS AND CONS OF LINEN
Linen is a natural fabric with a crisp clean look, but often harder to maintain than other fabrics because it wrinkles easily. Here are some pros and cons of linen fabric from MV Style (www.mvstylenaturals.com):
1. PROS: Natural fabric made from flax plant, highly absorbent so can remove perspiration from skin, good conductor of heat so in winter keeps heat in, but in summer feels cool to the touch, resists dirt and stains, pill resistant, contains natural antiseptic that prevents bacterial growth, and is strong.
2. CONS: Can be more expensive, creases/wrinkles easily, high shrinkage, must be ironed after washing.