Try the cable at this 50' length (unwind all the way as leaving wound may not be as accurate of a test) to see if it works for you (if not return it). If it works then you can paint it white
Mask the 2 gold-plated ends and spray it with flat (or glossy if you prefer) acrylic (enamel is more durable and flexible, but more messy, oil based, and takes much longer to dry) white paint. You could string the cable outside between trees (50' apart) tying it to trees using ropes or strings. With this cable stretched out just go back and forth to spray paint the entire cable. You can let it dry outside (pick a dry day obviously) before taking it down.
You could also dip the cable in a large paint trough (like those used for dipping wall paper in water), one section at a time until you get it all covered. To be perfect you have to let it dry before handling in between dips.
I think the outside hanging between trees is the cheapest, gives the best result, and is least messy. You could chose white glossy enamel (car paint) to make it look very nice and white. Since it's outside and already strung across 2 trees to paint and dry, using enamel is not a problem. This enamel paint will be much more flexible and last longer than acrylic which tend to chip/peel/crack off easier.
It'll be hard to find white HDMI cable at 50' length. You are pushing HDMI limit at that length with possible signal loss/loss of sync. on 1080p or 720p signals due to higher bandwidth requirement (1080i is close to 540p and should not be as much an issue--480p is even less bandwidth). You may want to consider using a repeater (not cheap) to boost the HDMI signal at that length. You can also use fiber optic type cabling for that length but this will be very expensive.