generally speaking in my advertising design job, private medical outfits like nurses and carers and mental health will usually adopt shades of green for their logos as its a very neutral soothing colour. it promotes the idea of peace and harmony.
also be very careful about using the translucent effects, as at letterheading size, they will tend to blur and logos do need to be sharp.
% shades of a single colour like a single green would also enable professional printing of the logo to be done in cheaper "spot" colour as opposed to the more expensive 4 colour CMYK process at a later date if required (when they realise that to print their own letterheads in any quantity is extortionately expensive on an ink jet desktop)
also generally speaking an earlier poster was correct. if u can make a logo work in mono first then the same logo will be easier to make work in colour.
Steve
edit:
after looking at the design again from a logo POV rather than a pixel one, i think if i were u i would try it without the ring too, u already have a ring in the shape of the 3 people to signify care and support. u could even tilt them slightly towards the angle the ring was at. the simpler the better for a logo tbh.
also 1 last thing u could even simplify the snake down to just a series of "S" shaped curves with no actual head in a similar style to your figures.