Can you sneak well in heavy armour?

Yeah, after you level up Sneak a lot and invest into its entire left-side perk tree. I've been successful a little bit right now with Sneak at about 39 and appropriate perks, but par for the course, you don't become truly invisible until you max it out.

Also, the Ebony Mail helps a lot, and that's heavy armour.

My first character was Heavy Armor and Sneak, I got past a lot of stuff undetected.

Like SystemsReady said, you need a high sneak and heavy armor skill. The muffle spell helps to reduce the amount of noise your armor makes.

Also, I found a nice explanation while doing a Google search (see below).

• Light Armor is easier to sneak in due to weight. It is also much faster to get the weightless perk in the Light armor tree, which negates the affect of wearing light armor while sneaking. The light armor perk is called 'Unhindered' and is 3 perks deep, requiring 50 skill in light armor.

• Heavy Armor is obviously, heavy. This makes it have a very noticeable affect on the ability to sneak while wearing it. The perk for weightless is deeper in the heavy armor tree compared to Light armor. The heavy armor perk is called 'Conditioning' and is 4 perks deep, and requires 70 skill in heavy armor.

Using Muffle, either as an enchantment or spell, helps with this a lot at lower levels, before your sneak gets high enough to off-set the armor.

I've found that walking instead of of running helps a bit too.

If you're lucky enough to have Muffle then yes. Otherwise, you need a high Sneak level.