If you're heading to North Wales weather is a huge factor, even in the height of summer. Last time I was there, the weather seemed really good, but it was so windy the Snowdon Mountain Railway only went halfway up.
This was the best shot I got considering you couldn't get off the train:
https://www.flickr.com/photos/alistairbeavis/15664820336/in/album-72157649075083435/
If you're walking, make sure you set off early, a) to try to get nice light (photographing in the midday sun (even if cloudy) isn't good) and b) to make sure you have time to get up and back down.
That 55-250mm lens isn't particularly heavy, but if you're struggling for bag space, I'd leave it behind in favour of something more important like food or a drink or something to keep you warm/dry.
As for making the best of the lens, try not to go above f8, keep your shutter speed up if hand holding as even a bit of wind-induced wobble will mean the photo comes out a little blurry.
Don't aim into the light, have the sun behind you if possible, otherwise you'll just get blown out skies and dark hills.
Look for whether the light is hitting the hills.
Here's one that some people might find controversial. Put on the lens hood.
Firstly it'll cut down on glare on the front element of the lens, meaning you'll get better contrast in your images.
Secondly, it'll keep a bit of rain off if that happens.
Thirdly, if you happen to drop the camera or bump it into something or someone while walking, it'll protect the lens element from getting scratched.
One last thing unrelated to lenses, take or leave it.
If you're walking with other people, you don't want to be holding them up every time you stop to take a photo, so, I'd suggest you don't keep getting your camera out then putting back into your bag each time. It wastes time which might annoy your companions and you may miss that brief sunny spell between clouds.