What is the scene that is brought to the reader's mind on reading the first 4 lines of the poem?

I leant upon a coppice gate
     When Frost was spectre-gray,
And Winter's dregs made desolate
     The weakening eye of day.

To get an emotional feel for the tone of the poem, try reading the four lines aloud several times, and exaggerate the stressed and unstressed syllables. This way you may detect which words stand out because of the stresses.  Look at the stressed syllables below:

I LEANT u-PON a COP-pice GATE

when FROST was SPEC-ter GRAY

and WIN-ter's DREGS made DES-o-LATE

the WEA-kening EYE of DAY.

Note the vowel sounds in the last word of each line: gate, gray, desolate (with emphasis on "--late"), and day--what vowel sound do they all have in common? These vowel sounds seem to elongate, or to draw out the words, and thus slow the rhythm of the poem, enhancing its serious, sombre, and, yes, desolate tone.

If you don't know any of the words, look them up. What is a coppice gate, you ask? Well, a coppice is a small grove, or a small enclosed thicket or growth of trees. The speaker establishes a point of view as he draws us into the scene: he leans upon a gate, looking at the grove. There is a sense of separateness and loneliness of the onlooker gazing at the scenery before him, and the reader joins him in this lonesome perception.

Secondly, "when Frost was specter gray"--we have figurative language here because frost is capitalized. Thus the speaker elevates frost as a natural phenomenon by personifying it, capitalizing it as a proper name. Frost is specter gray.  What feeling does a specter evoke in you? We are talking about a ghost--ghostly gray.  Frost resembles death in the way it wipes out anything living in its presence.  Anything Frost touches turns into gray ghostly nothingness just like Frost itself--its presence is ominous.

And then pay attention to syntax, or sentence structure. Who is doing what? Who is the subject of the sentence? What is he doing? To whom?  "And winter's dregs made desolate the weakening eye of day" Turn this around to a normal sentense order: Winters dregs made the weakening eye of day desolate. Better.

Look up "dregs" if you aren't sure what it is. It is the last remaining part of something, so the last parts of winter may be the ending of it, the last days of that period or season. 

"Weakening eye of day" is a metaphor, that is comparing two unlike things, or saying that the day has an eye. The sun is compared to a day's eye, and it is weakening because the daylight is coming to an end, or it is the late winter evening when the sun is going down.  Therefore, the last remains of winter are making even the last rays of sunlight seem sad, lonesome, desolate, desperate.

There is lots of information in these four lines. Take the images one at a time and see what feeling they create. It's not just a cold winter day. It is gloomy, hopeless, dead as if no life can ever spring from the vast, dark, gray desolation.

Good luck.