Defining "1e feel" is as hard as defining why some people feel 4e, or 3e, or Xe, is "just not D&D to me". Very hard to do, very subjective, and very unique to individuals.
That said, I think:
1e is Greyhawk instead of Ptolus (thank you Filcher)
1e is medieval, not anime
1e is complex dungeons, not complex politics
1e is tattooed Frost barbarians, not dragonmarked artificers
1e is dangerous "peasant to hero", not "hero to god"
In 1e, if you wanted to do something "different", you explained yourself. The DM weighed what you said, thought about Gygaxian guidelines, and spit out an answer or a relevant check. There was not a codified rule for any move you could think of.
If we put this in a "power spectrum" of decisions that fall with the DM as opposed to rules that players can hold up, it'd probably look like:
DM Power ------------------------------------ PC Power
------1E-----------------------------------------------
-------------2E----------------------------------------
-------------------------------------------3E----------
----------------------4E-------------------------------
"Power" is a poor word, I know, but I'm trying to show where the heart of authority lies with how an action is adjudicated. 4e opens that up quite a bit over 3e, for better or worse (according to personal preference). I happen to think 3e made so many rules for so many actions because there was, or is, a dearth of DMs out there who can and will make decisions that are fair and equitable, and there is a dearth of players out there who can accept such decisions without feeling they are slighted.
Some lucky groups, certainly, have a good symbiosis. A DM that is fair and does make judgments, and players that accept those judgments because they know it's not an adversarial situation.
This ambiguous "1e feel" isn't for everyone, certainly. And my explanation of that feel is just that - mine. You could probably ask 42 different guys who cut their teeth on 1e what that "feel" is all about, and they'd tell you 42 different things.
WP