Hard to tell exactly without listening to the issue. Have you had this issue when not recording on windy mountains? If not, then yes, it may be the windscreen.

I find the foam windscreens like the one that comes with the H4n to be more of a spit guard than a usable windscreen in anything more than a slight breeze. You need something with a longer fur to diffuse the wind before it hits the mic diaphragm. These RedHead Windscreens have been recommended around here before for the H4n and I believe one or two members have gone the DIY route, just buying the fabric and sewing one together.

If you have had the issue off the mountain then you may be setting the gain too high and what you're hearing is the noise floor of the unit itself. Although I would imagine that with high gain in a windy situation the bigger problem would be clipping & distortion with each gust of wind... Try getting closer to the sound source that you're hoping to capture and pull back the gain a bit.

If you post a short clip of the issue up to soundcloud and link to it here we may be better able to diagnose your particular issue.

couple of things i learned the hard way

• when it comes to wind, don't trust headphones. put on a windshield of the hairy kind. zeppelins suspend the mic floating in the middle of still air. that's the best. -countryside ambiences will give you hiss on a portable recorder. it's just too darn quiet compared to the city bustle so the gain is up there.. low-pass it, you have a chance of getting a useful recording.
• recording quietness in 96khz on a portable unit has a chance of catching its power system noise.
• when listening back via monitors, always download the file to your computer first. my Sony's internal output has its own hiss which is not on the recording.

hope this helps

I have the old H4, and in my experience it is too noisy for low level ambiences. It is really great if you are recording loud or medium loud ambiences. You should record at 96k to get the most from your equipment, but the noise floor is still pretty high.

My best experiences with the H4 have been with external microphones, Sennheiser MKH 40/30 MS setup or Schoeps MS. These mics are very good and the noise floor is a lot lower.

If you use the internal mics, I recommend just slipping the whole recorder inside a fur from a zeppelin, put it into record and place it on a rock or the roof of a car, so you don't get any handling noise.

OK I understand your problems with wind with the ZOOMH4N: Even with a wind shield, if the wind is strong, it won't be enough with the windshield that comes with the recorder. I also strongly recommend getting a shield that match the onboard mics.

The wind noise you normally get with the zoom machine is a very characteristic low rumble, not a HISS. If you can post the hiss online I can have a listen.

Is your sound source loud enough? Hiss normally becomes evident with the Zoom when you crank up the gain quite a bit. I try and use the gain below 50% if using the onboard mics. (they aren't the best condensers out there.

If you can get a couple of condensers to use with it- and you don't mind carrying them around the mountains!- then you are guaranteed a better quality recording, with higher levels and, with good wind-shields, a wind-free recording too!