Hath not old custom made this life more sweet
Than that of painted pomp? Are not these woods
More free from peril than the envious court?
Here feel we but the penalty of Adam,
The seasons' difference, as the icy fang
And churlish chiding of the winter's wind,
[...]
'This is no flattery: these are counsellors
That feelingly persuade me what I am.' (II.i)

Speaking to his "brothers in exile," Duke Senior uses the Biblical allusion, "the penalty of Adam," to refer to the exile of Adam (with Eve) from the Garden of Eden after their fall from grace. With this allusion, Duke Senior likens his exile to Adam's exile and likens himself to Adam. He goes on with negative interrogatory (negative questions: "hath not" "are not") to set forth his optimistic opinion that he and his exiled men live better in the Forest of Arden than they did at court. He rejects the "painted pomp" of court. He speaks of the "envious court" as being "perilous": "envious" means there were those who wanted what others had; "perilous" means that the envious ones were dangerous and would stop at nothing to get what they wanted, for example, Duke Frederick who stripped Duke Senior of his belongings and exiled him.

Leading into the allusion, Duke Senior goes on to say that  in Arden the only perilousness they feel is what Adam felt: "Here feel we but the penalty of Adam." He defines what this is by speaking of the change in seasons and the "icy fang" of "winter's wind." In other words, Adam's penalty was his exile to live out of doors in the eye of the seasons' tempests, especially noting the winter's cold and wind. He concludes his speech by equating Adam's penalty--the seasons' changes and the wintry blasts--with counselors. He says that Adam's penalty does not vainly flatter the Duke to get what "perilous envy" desires. Adam's penalty councils truly, thus teaching Duke Senior what he truly is. What Duke Senior is truly is someone who sees "Sermons in stones and good in every thing."

Thus that very simple Biblical allusion, "the penalty of Adam," about what Adam suffered in his exile, leads to a very important discussion of Shakespeare's themes of how to live and of court versus forest. To put it a little differently, the allusion to Adam's exile and nature living leads to a discussion of perilous pomp versus humble, truthful living.

In his famous speech at the beginning of Act II, Scene 1 of As You Like It, Duke Senior asks, "Here feel we but the penalty of Adam." He is referring to Adam in Genesis who was banished from the Garden of Eden along with Eve for eating the forbidden fruit. The Garden of Eden was a paradise in which, though naked, Adam and Eve were never cold--but part of their penalty for disobeying God was to be exposed to what Duke Senior describes as

The season's difference, as the icy fang
And churlish chiding of the winter's wind,
Which, when it bites and blows upon my body
Even till I shrink with cold, I smile and say
"This is no flattery"; these are counselors
That feelingly persuade me what I am.

When the Duke says "feel we but," he does not mean "here we do not feel" but "here do we not feel?" and "here we feel only the penalty." In the lines immediately preceding "Here feel we but the penalty of Adam," he asks

Are not these woods
More free from peril than the envious court?

So, "Here feel we but the penalty of Adam" is spoken in the same spirit, although perhaps not as a question since there is no question mark, so it might be confusing.

The quote reference is Duke Senior referring to Adam in Genesis and asking several of his loyal followers, in effect, "Do we not have to endure the cold weather, just like Adam after he was banished from the Garden of Eden, and isn't this actually beneficial, since it makes us realize how unimportant we all are and how much there is still left to us to enjoy in nature?"

What follows in this speech is one of Shakespeare's wisest and most beautiful similes:

Sweet are the uses of adversity,
Which, like the toad, ugly and venomous,
Wears yet a precious jewel in his head

The Duke is definitely not referring to the character named Adam, who is a servant of Orlando, but to the Adam of the Bible.