Wa alaikum asalaam.
This is from the Hanafi perspective:
In the Hanafi school, the dog is not essentially filthy (najis al-`ayn), unlike pigs. [Haskafi, al-Durr al-Mukhtar]
As such, if one’s clothes come into contact with a wet dog’s body, no filth will be considered to have transferred to one.
However, the saliva of dogs is filthy because the ruling of saliva follows the ruling related to the flesh of the given animal. [ibid. and al-Fatawaa l-Hindiyya, quoting Nasafi’s Kanz]
As such, if a dog licks one’s clothes, the area licked would need to be washed three times or under flowing water, like other filth.
It would be recommended to wash it seven times, one of them with water admixed with soil, to follow the outward purport of the instruction of the Prophet (Allah bless him & give him peace), and to avoid the difference of opinion of the Shafiis and Hanbalis (Allah be well pleased with their scholars, and benefit us from the baraka of all the inheritors of the Prophet’s way). [Buhuti,Kashshaf al-Qina`; Nawawi, Minhaj al-Talibin] [The Hanafi imams understood the Prophet’s command to be for emphasis and recommendation, not obligation.]
Source:
Sunnipath
And this is from the Shafi'i perspective:
It is obvious that acquiring a dog without need is haram and it prevents the angels of mercy from entering the place that they are in. Likewise, acquiring pictures of things that could have souls, such as pictures of humans and animals is haram, and it also prevents those angels from entering, as we said.
However, their presence does not affect the validity of the prayer, so whoever prays in a place that has a dog or pictures, his prayer is valid and he does not need to repeat it. It seems that a room that does not have pictures or a dog would be entered by the angels of mercy, because it does not contain anything prohibited in it, and Allah knows best.
[s. If the moisture from a dog (or dry dog hair) affects one�s person, clothes or place of prayer, one�s prayer would be invalid, until he purified them, see Reliance of the Traveller, e14.1(14), e14.7 and f4.0.]
Source:
Sunnipath
Hope that helps.
Nur-ud-Dean