Cottonwood Terrace Apartments for rent in Colorado Springs, CO on ForRent.com: (866) 544-0364 - Availability, pricing and special promotions subject to change daily. Cottonwood Terrace is located in the Briargate area. Each apartment home has been designed to suit your active lifestyle. Unlike many apartment homes, Cottonwood Terrace is located in a residential neighborhood within minutes of restaurants, banks, and shopping.andnbsp; The sparkling pool, outdoor spa, and 24 hour exercise facilities can make daily fitness and relaxation seem second nature.