Isn't killing a deer for its golden skin unjustified?
In Rāma's case, it's not unjustified. Revealing her second boon to Daśaratha, Kaikeyī says the following:
नव पञ्च च वर्षाणि दण्डकारण्यमाश्रितः || २-११-२६
चीराजिनजटाधारी रामो भवतु तापसः |
Rama has to take refuge in the forest of Dandaka for fourteen years and let him become an ascetic wearing rags, deer skin and matted hair.
चीरा (cīrā) means 'piece of cloth' and अजिन (ajina) means 'skin of a wild animal.'
So, clearly, in those days, when you live in a forest, that's your usual attire. Rāma was simply following the norms of his day. Hunting, meat-eating, using deerskin as a mat or as a coat to protect oneself from the weather was all normal for forest dwellers.
Also, from Bhagavad-gītā (Ch. 6: Dhyāna-yoga 11-12), we have:
To practice yoga, one should go to a secluded place and should lay kuśa grass on the ground and then cover it with a deerskin and a soft cloth. The seat should be neither too high nor too low and should be situated in a sacred place. The yogī should then sit on it very ﬁrmly and practice yoga to purify the heart by controlling his mind, senses and activities and ﬁxing the mind on one point.
Now, one should not misinterpret the above to mean one cannot do yoga without getting a deerskin first, and ignoring other more important instructions.
In your comment, you also ask:
Where is it said that Kshatriyas are allowed to hunt in Vedas?
Stating his opinion in Anuśāsana-parva of the Mahābhārata, this is what Bhīṣma says:
It is even so, O mighty-armed one, as thou sayest. There is nothing on earth that is superior to flesh in point of taste. There is nothing that is more beneficial then flesh to persons that are lean, or weak, or afflicted with disease, or addicted to sexual congress or exhausted with travel. Flesh speedily increases strength. It produces great development. There is no food, O scorcher of foes, that is superior to flesh.
Hence, O Bharata, even royal sages betake themselves to the practice of hunting. By such conduct they do not become stained with sin. Indeed, the practice is not regarded as sinful.
In the earlier chapter, he says:
Many kings in ancient days, O son of Pritha, who had constituted themselves the souls of all creatures and who were conversant with the truths of all things, viz., Soul and Not-soul, had abstained from flesh either for the whole of the month of Karttika or for the whole of the lighted fortnight in that month. They were Nabhaga and Amvarisha and the high-souled Gaya and Ayu and Anaranya and Dilipa and Raghu and Puru and Kartavirya and Aniruddha and Nahusha and Yayati and Nrigas and Vishwaksena and Sasavindu and Yuvanaswa and Sivi, the son of Usinara, and Muchukunda and Mandhatri, and Harischandra. Do thou always speak the truth. Never speak an untruth. Truth is an eternal duty. It is by truth that Harischandra roves through heaven like a second Chandramas. These other kings also, viz., Syenachitra, O monarch, and Somaka and Vrika and Raivata and Rantideva and Vasu and Srinjaya, and Dushmanta and Karushma and Rama and Alarka and Nala, and Virupaswa and Nimi and Janaka of great intelligence, and Aila and Prithu and Virasena, and Ikshvaku, and Sambhu, and Sweta, and Sagara, and Aja and Dhundhu and Suvahu, and Haryaswa and Kshupa and Bharata, O monarch, did not eat flesh for the month of Karttika and as the consequence thereof attained to heaven...
When we see Rāma and Kṛṣṇa as kṣatriya kings & in light of above statements, their actions are justified.
Now Bhīṣma also says:
13,117.037a ahiṃsā paramo dharmas tathāhiṃsā paro damaḥ
13,117.037c ahiṃsā paramaṃ dānam ahiṃsā paramaṃ tapaḥ
13,117.038a ahiṃsā paramo yajñas tathāhiṃsā paraṃ balam
13,117.038c ahiṃsā paramaṃ mitram ahiṃsā paramaṃ sukham
13,117.038e ahiṃsā paramaṃ satyam ahiṃsā paramaṃ śrutam
Abstention from cruelty is the highest Religion ... is the highest self-control.
Abstention from cruelty is the highest gift ... is the highest penance.
Abstention from cruelty is the highest sacrifice ... is the highest puissance.
Abstention from cruelty is the highest friend ... is the highest happiness.
Abstention from cruelty is the highest truth ... is the highest Sruti.
But that is only possible for sages:
13,116.073a madhu māṃsaṃ ca ye nityaṃ varjayantīha dhārmikāḥ
13,116.073c janmaprabhṛti madyaṃ ca sarve te munayaḥ smṛtāḥ
These righteous men who, from the time of birth, abstain from honey and meat and wine, are regarded as Munis.
In conclusion, we should avoid judging characters in Hindu scriptures based on current trends and also mixing duties and living styles of different varṇas (kṣatriyas, brāhmaṇas, etc.) or of sannyāsīs.