I used:

• Stream.cycle/1 to handle the repeating horizontal values
• Enum.take_every/2 to handle skipping the downward slope.
• The input wasn’t very long, so I just brute forced the horizontal value with Enum.at/2.

  def slope(v_x, v_y) do
    {_, trees} =
      File.read!("input")
      |> String.trim()
      |> String.split("\n")
      |> Enum.take_every(v_y)
      |> Enum.map(&String.to_charlist/1)
      |> Enum.reduce({0, 0}, fn row, {x, trees} ->
        trees =
          case Stream.cycle(row) |> Enum.at(x) do
            ?# -> trees + 1
            ?. -> trees
          end

        {x + v_x, trees}
      end)

    trees
  end

I see I’m not the first one to find the Stream.cycle function
My version:

defmodule Aoc2020.Day03 do
  def part1(input) do
    count_trees(input, {3, 1})
  end

  def part2(input) do
    slopes = [
      {1, 1},
      {3, 1},
      {5, 1},
      {7, 1},
      {1, 2}
    ]

    for slope <- slopes, reduce: 1 do
      product -> product * count_trees(input, slope)
    end
  end

  def count_trees(input, {dx, dy}) do
    input
    |> Stream.take_every(dy)
    |> Stream.map(&Stream.cycle/1)
    |> Enum.reduce({0, 0}, fn
      row, {trees, shift} ->
        row
        |> Stream.drop(shift)
        |> Enum.at(0)
        |> case do
          ?. ->
            {trees, shift + dx}

          ?# ->
            {trees + 1, shift + dx}
        end
    end)
    |> elem(0)
  end

  def input_stream(path) do
    File.stream!(path)
    |> Stream.map(&parse/1)
  end

  defp parse(line) do
    line
    |> String.trim()
    |> String.to_charlist()
  end
end

input = Aoc2020.Day03.input_stream("input.txt")

input
|> Aoc2020.Day03.part1()
|> IO.inspect(label: "part1")

input
|> Aoc2020.Day03.part2()
|> IO.inspect(label: "part2")

My solution with streams keeping only 1 line of map in memory at any given time.

defmodule Event3 do
  def run do
    part1_ruleset = [{3, 1}]
    part2_ruleset = [{1, 1}, {3, 1}, {5, 1}, {7, 1}, {1, 2}]
    IO.puts("Test part1: #{solver("input/event3/test.txt", part1_ruleset)}")
    IO.puts("Puzzle part1: #{solver("input/event3/puzzle.txt", part1_ruleset)}")
    IO.puts("Test part2: #{solver("input/event3/test.txt", part2_ruleset)}")
    IO.puts("Puzzle part2: #{solver("input/event3/puzzle.txt", part2_ruleset)}")
  end

  def solver(path, ruleset) do
    accs = Enum.map(ruleset, &rule_to_acc/1)

    input_stream(path)
    |> Stream.drop(1)
    |> Stream.transform(accs, &step_all/2)
    |> Stream.take(-length(ruleset))
    |> Stream.flat_map(& &1)
    |> Enum.reduce(&(&1 * &2))
  end

  def input_stream(path), do: path |> File.stream!() |> Stream.map(&parse_input/1)

  def parse_input(input), do: String.trim(input) |> String.graphemes() |> Enum.map(&(&1 == "#"))

  def step_all(input, acc), do: Enum.map(acc, &step(input, &1)) |> Enum.unzip()

  def step(input, {count, index, step, step_down, step_down}) do
    width = length(input)
    count = count + ((Enum.at(input, index) && 1) || 0)
    {[count], {count, rem(index + step, width), step, step_down, 1}}
  end

  def step(_input, {count, index, step, step_down, down_counter}),
    do: {[count], {count, index, step, step_down, down_counter + 1}}

  def rule_to_acc({right, down}), do: {0, right, right, down, 1}
end