Colour represents the specific attribute of a deity. I'm giving here example from different colours of Lord Shiva:
1) Purely white SadaShiva:
SadaShiva is purely white as discussed in answer here. White colour here represents that SadaShiva is eternally pure and untouched by the Tri-Gunas (satwa-rajas-tamas) of Maya.
नीलग्रिवं पञ्चवक्त्रं त्रयम्बकं चन्द्रशेखरम् ।
वामांगे बिभ्रतं गौरीं विद्युतपुञ्ज समप्रभाम् ।।
कर्पूरगौर गौरिशं सर्वालंकारधारिणम् ।
सितभस्मलसद्देहं सितवस्त्रं महोज्जवलम् ।। (Shiva Purana Mahatmyam, Chapter 4)
His neck had a blue hue ; he had five faces, three eyes , the cresent moon as crest-ornament and his left hand was apportioned to Gauri , who had the brilliance of lighting. He was white in complexion like camphor and wore all ornaments. Besmeared with white ashes all over the body and clad in white clothes,he shone brilliantly.
Shivam represents the Turiya state which is beyond realm of Maya as I discuss here. Hence pure white colour of Sada-Shiva rightly represent it.
2) Aditya Varnam Rudra (Golden Coloured Rudra):
There is also one form of Lord Shiva which is of Aditya Varnam (golden colour). I discuss it also in my answer here.
देवा वै रुद्रं स्वर्गं लोकं गतं न व्यजानन्न् आदित्यवर्णं चरन्तन् | (Katha Aranyaka 2.100)
Indeed the deva-s did not recognize Rudra who had entered the heavenly world wandering in Aditya Varnam (Solar/Golden Lusture)
Similarly the SataRudriya hymn stating (Namo Hiranyabaahave / Salutations to him who has golden arns) and the Taittariya Aranyaka:
नमो हिरण्यबाहवे हिरण्यवर्णाय... (Taittariya Aranyaka 10.22)
Salutations to him who has Golden arms and Golden complexion..
And the RigVeda also as I discuss in my answer here:
हिरण्यम् इव रोचते
Shining like the bright gold.
शुक्र इव सूर्यो
Shines like the Sun.
This Golden complexion of Lord represents the Purusha attribute of Lord:
वेदाहमेतं पुरुषं महान्त-
मादित्यवर्णं तमसः परस्तात् ।
नान्यः पन्था विद्यतेऽयनाय ॥ ८॥ (RigVeda 10.90, Svet. Up. 3.8)
I know the great Purusha, who is of Aditya Varna and beyond darkness. Only by knowing Him does one pass over death; there is no other way to the Supreme Goal.
3) Nila-Lohita Rudra (The Blue and Red Rudra):
There is also another form of Lord Shiva which is half blue and half red and called as Nilalohita:
द्रापे अन्धसस्पते दरिद्रन्नीललोहित (YajurVeda 16.47)
Oh you who punishes as per sin of people. Oh! Lord of Food. Oh! NilaLohita.
The blue and red colour form of Lord also has special significance which I discuss here.
ललाटमस्य निर्भिद्य प्रादुरासीत्पितामहात् ।
लोहितोऽभूत्स्वयं नीलः शिवस्य हृदयोद्भव ।।
वह्रश्चैव तु संयोगात्प्रकृत्या पुरुषः प्रभुः ।
नीलश्च लोहितश्चैव यतः कालाकृतिः पुमान् ।।
नीललोहित ईत्युक्तस्तेन देवेन वै प्रभुः ।
All pervading lord born of body of Bhava, came out of Brahma by piercing his forehead. The lord who born of the heart of Shiva was originally blue but became red coming in contact with fire. It represents the form of combination of Prakriti and Purusha of the Lord. Because of the form with both blue and red colour resembling Kãla, Lord came to be known by the name NilaLohita.
Thus the Nila-Lohita form of Lord represents the Union of Prakirti and Purusha.
There are also other coloured forms of Lord Shiva which has it's own meaning. It is already proved that these colours have special meaning and colour of God shows that meaning.
Lord Vishnu is dark-blue in colour. I'm sure it has also it's special meaning. I scanned searched in three puranas; Srimad Bhagvatam, Vishnu Purana and Padma Purana. They call Vishnu as 'dark-blue' colour many many times but they do not give meaning of the colour. I think Pancharatra Scriptures discuss about this thing. I'll update the answer when I find any reference from scripture regarding meaning of colour of Lord Vishnu.