洗濯(物)が溜まる is a very common way to say "to have a lot of clothes to wash". It implies you have to wash that laundry soon.
If you do want to emphasize the physical aspect of the pile of the laundry, 洗濯物が積もる may be technically OK. You might say 「洗濯物が山のように積もっていて(or 山のように積んであって)、ドアが開けられない!」 when the laundry is physically blocking the door :)
雪が積もる is more common, and it means a certain area is uniformly covered by snow after a snowfall. If you see a layer of snow on a car after a snowy day, you can say "車の上に雪が積もっている". You can modify this sentence with adverbs like 深く, たくさん, いっぱい, 少し, etc.
雪が溜まる (or noun 雪【ゆき】溜【だ】まり) refers to the localized, irregular accumulation of snow, due to wind or other environmental/topographical reasons. If you see remaining snow under the car, several days after the snowfall, then you can say "(まだ)車の下に雪が溜まっている". If there's a lot of such snow, you can say たくさん／大量に／いっぱい溜まっている, but not 深く溜まっている.
The difference between "埃【ほこり】が積もる" and "埃が溜まる" is the same (埃 = dust). 積もった埃 is seen on a flat floor, and 溜まった埃, behind a bookshelf or in my PC.